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Netica-J Reference Manual

1. abnormal 11 0 normal 89 0 1 Dolnference java Example use of Netica J for doing probabilistic inference af import norsys netica public class Dolnference public static void main String args try Environ env new Environ null Read in the net created by the BuildNet java example program Net net new Net new Streamer Data Files ChestClinicBuilt dne 24 NETICA API JAVA VERSION 4 18 Node visitAsia net getNode VisitAsia Node tuberculosis net getNode Tuberculosis Node xRay net getNode XRay net compile double belief tuberculosis getBelief present System out printin nThe probability of tuberculosis is belief xRay finding enterState abnormal belief tuberculosis getBelief present System out printin nGiven an abnormal X ray n the probability of tuberculosis is belief visitAsia finding enterState visit belief tuberculosis getBelief present System out println nGiven an abnormal X ray and a visit to Asia n the probability of tuberculosis is belief n net finalize catch Exception e e printStackTrace The program starts by using new Environ as described in the previous chapter Next new Net is used to read the file and create the net in memory If you wish to have detailed descriptions of any of these functions remember that you can look them up in the
2. 70 NETICA API JAVA VERSION 4 18 System out print If the forecast is cloudy System out println the expected utility of umbrella state 0 is utils O of umbrella state 1 is utils 1 n 2nd type of usage To get the optimal decision table net retractFindings umbrella getExpectedUtils II causes Netica to recompute decision tables II given current findings which in this case are no findings for int fs 0 fs lt forecast getNumStates fs int parStates new int 1 parStates 0 fs II forecast is the parent of umbrella int decision umbrella getStateFuncTable parStates null 0 System out printin If the forecast is forecast state fs tthe best decision is umbrella state decision net finalize free resources immediately and safely not necessary but a good habit catch Exception e e printStackTrace Once the net is built the program calls Net compileQ and then Node getExpectedUtils to force a belief updating which will build a new deterministic table for each decision node Each deterministic table represents a function which provides a value for the node for each possible configuration of parent values Since the links into a decision node indicate what the decision maker will know when he is about to make the decision this function provides a decision for each possible information state The decision functions N
3. p Color Taste Taste sweet Color red 0 9 0 1 0 5 For more examples see the Specialized Examples section below 11 2 Equation Syntax Netica equations follow most of the usual standards for mathematical equations and are similar to programming in Java C or C The usual mathematical operators etc and the usual functions min abs sin etc can be used parenthesis are used for grouping and numeric constants are in their usual form e g 3 4 2 5 3e 12 Left Hand Side For a deterministic node the part of an equation to the left hand side of the equals symbol consists of the name of the node an open parenthesis a list of the names of the parents separated by commas and a close parenthesis if you have defined link names you must use those instead of parent names For instance if the equation is for node Position and the parents of Position are Velocity Time and Mode the left hand side could be Position Velocity Time Mode Note that the spaces are not required there may be more spaces if desired and the parents can be in any order For probabilistic nodes i e chance nodes the left hand side consists of a lower case p an open parenthesis the name of the node a vertical bar a list of the names of the parents or link names separated by commas and a close parenthesis If the node mentioned above had been a probabilistic node the left hand side of its equation
4. 98 Fisher Tippet distribution eqn function 98 Flow Instrument example 61 for n N conditions no warning message 87 formula 84 Fortran 6 forward sampling 22 F ratio distribution eqn function 98 frequency of cases 37 functionality 7 fuzzy logic 49 G gamma eqn function 98 gamma distribution eqn function 98 GammaDist eqn function 98 Gaussian in UVF file 42 generateRandomCase Net 22 83 84 in use 38 geometric distribution eqn function 98 GeometricDist eqn function 98 getBelief Node 25 in use 23 getBeliefs Node in use 35 getBytes User 80 getConfusion NetTester 57 in use 57 getErrorRate NetTester 57 in use 57 getExpectedUtils Node 70 in use 68 getInputIndex Node in use 63 getLikelihood Node Value in use 35 getLogLoss NetTester 57 in use 57 getMutuallnfo Sensitivity 82 getNodes Net in use 38 52 getNthFieldName User 80 81 getNumber User 80 getObject User 80 getQuadraticLoss NetTester 57 getReference User 80 getRelatedNodes for a group of nodes 80 getRelatedNodes Node 79 getState Node Value 36 in use 35 getStateFuncTable Node 70 in use 68 NETICA API 115 getString User 80 getVarianceOfReal Sensitivity 82 gradient descent learning algorithm 49 when to use 47 graph algorithms 79 graphical model 6 20 graphical user interface 6 H Hugin
5. A negative finding can be represented easily by just listing the state s eliminated by the observation Likelihood Syntax Si Pa S2 Po Sn Pn each s is a state name state index preceded by Gaussian interval or unbounded interval Each p is a number between 0 and 1 Some p may be absent Examples female 8 male 3 3 1 0 2 74 2 0 4 Ora eS eUS 135 10 0 4 other Gea This is the same as a set of possibilities but each possibility is weighted with a likelihood that appears after it separated by a space Since the numbers are likelihoods they do not need to sum to one The most common type of likelihood vectors are for discrete variables where each state is listed followed by its likelihood Any states that appear without a number have a likelihood of 1 and any states that don t appear at all have a likelihood of 0 Arbitrary likelihood distributions for continuous variables can be formed by a series of adjacent intervals each with its own probability Or the elements can overlap and then their likelihoods are combined For example 0 10 1 2 4 2 would be the combination of a rect function extending from 0 to 10 with height 0 1 and another rect from 2 to 4 with a height of 0 2 Another useful distribution that is easy to form is a weighted combination of Gaussians For example 3 1 0 2 7 2 0 4 is a bi modal distribution with peaks at 3 and 7 It is possible to mix weighted Gaussians intervals and
6. LA Continuous Probability Distribution the first argument is a continuous variable that the distribution is over approx_eq x y x y eqnear 2e 5 x y where x and y are unrestricted real numbers Returns TRUE iff x is equal to y within a small relative tolerance Usually the operator form of this function is most convenient x y It is meant for comparing computed real number values that might not be exactly equal due to slight numerical inaccuracies To have control of the tolerance use eqnear argmax0 Xo X1 Xn i s t Xi xj for all j argmaxl X X2 Xn where x are unrestricted real numbers Returns the index position in list of the argument with the highest value If there are several with the same highest value then the index of the first occurrence will be returned The first argument has index 0 if argmax0 is used or index 1 if argmax1 is used At least one argument must be passed See also max argmin select Example argmax0 1 6 6 3 4 1 26 3 4 returns 2 argmaxl 1 6 6 3 4 1 26 3 4 returns 3 96 NETICA API JAVA VERSION 4 18 argminO Xo X1 Xn i s t x lt xj for all j argminl x1 X2 Xn where x are unrestricted real numbers Returns the index position in list of the argument with the lowest value If there are several with the same lowest value then the index of the first occurrence will be returned The first argument has index 0 if argmin0O is used or
7. import java io File import norsys netica int numCases 200 try public class SimulateCases public static void main String args the probability distribution given by a Bayes net Environ env new Environ null Example use of Netica J for generating random cases that follow System out printin Creating numCases random cases Read in the net created by the BuildNet java example program cv CT cr eT EP CT Dyspnea presen presen presen absent presen presen presen presen Cr te et E PA cv EN JAVA VERSION 4 18 NETICA API 39 Net net new Net new Streamer Data Files ChestClinicBuilt dne NodeList nodes net getNodes new File Data Files ChestClinic cas delete since ChestClinic cas may II exist from a previous run and we do not wish to append Streamer caseFile new Streamer Data Files ChestClinic cas net compile for int n 0 n lt numCases n net retractFindings int res net generateRandomCase nodes 0 20 if res gt 0 net writeFindings caseFile nodes n 1 0 net finalize catch Exception e e printStackTrace First the program reads in the same net that we built in the Building and Saving Nets chapter Then it deletes a file named ChestClinic cas if there is one otherwise it would try to add the cases to this file Then in a loop repeated 20 times
8. of the Netica API family and to obtain their documentation The C version can be used by programs written in any language which can call C functions such as C Python Perl Prolog Lisp Matlab Delphi Pascal Fortran or Cobol Interface files for some of these languages developed by the Netica community are available from Norsys Matlab is supported through this the Java API This manual assumes that you are familiar with the Java programming language It also assumes familiarity with Bayesian networks or influence diagrams although it has a little introductory material especially on issues that are new or generally not well understood Questions and comments about material in this manual may be sent to netica j norsys com 1 1 Netica Java API The Netica J API is a complete library of Java classes for working with Bayesian networks also known as Bayes nets belief networks graphical models or probabilistic causal models and influence diagrams also known as decision networks It contains functions to build learn from data modify transform erformance test save and read nets as well as a powerful inference engine It can manage cases and p 2 bi JAVA VERSION 4 18 NETICA API 7 sets of cases and can connect directly with most database software Bayes nets can be used for diagnosis prediction classification sensor fusion risk analysis decision analysis combining uncertain information and numerous probabilis
9. 12 hypergeometric distribution eqn function 99 HypergeometricDist eqn function 99 IDE installation 12 ideas for improvement 13 IDname 29 IDnum 37 ignorance 49 include_evidence_nodes passed to getRelatedNodes 79 increasing eqn function 99 increasing eq eqn function 99 independence degree of 81 finding 79 independent finding 34 inference functions available 106 influence diagram 6 67 influence degree of 81 inheriting from Node or Net 16 input names in equation 89 input output done by Netica API 7 insertFindings DatabaseManager 41 installing Netica J 11 Instrument example 61 intersection passed to getRelatedNodes 79 interval in UVF file 43 isRelated Node 80 J Java 6 Java version required 11 javadocs 10 12 join tree junction tree 22 versus node absorption 22 K knowledge base 20 116 L Laplace distribution eqn function 99 LaplaceDist eqn function 99 large nets too big to compile 22 latent variable 47 layout of nodes 61 learnCPTs Learner 54 in use 41 54 LearnCPTs java example program 52 LearnCPTs java file 10 Learner class 107 Learner constructor 54 in use 41 learning adaptive 55 Bayes nets 46 from cases 46 parameter 46 structure 46 learning algorithms 47 learning from data functions available 107 learning nodes 47 LearnLatent cas file 10 LearnLatent java file 10 l
10. Example use of Netica J to construct a Bayes net and save it to file import norsys netica import norsys neticaEx aliases Node public class BuildNet public static void main String args 28 try NETICA API JAVA VERSION 4 18 Node setConstructorClass norsys neticaEx aliases Node Environ env new Environ null Net net new Net net setName ChestClinic Node visitAsia new Node VisitAsia visit no_ visit net Node tuberculosis new Node Tuberculosis present absent net Node smoking new Node Smoking smoker nonsmoker net Node cancer new Node Cancer present absent net Node tbOrCa new Node TbOrCa true false net Node xRay new Node XRay abnormal normal net visitAsia setTitle Visit to Asia cancer setTitle Lung Cancer toOrCa setTitle Tuberculosis or Cancer visitAsia state visit setTitle Visited Asia within the last 3 years tuberculosis addLink visitAsia puts link from visitAsia to tuberculosis cancer addLink smoking tbOrCa addLink tuberculosis tbOrCa addLink cancer xRay addLink tbOrCa visitAsia setCPTable 0 01 0 99 smoking setCPTable 0 5 0 5 II VisitAsia present absent tuberculosis setCPTable visit 0 05 0 95 tuberculosis setCPTable no_ visit 0 01 0 99 II Smoking present absent cancer setCPTable smoker 0 1 0 9 cancer setCPTable nonsmoker
11. One exception to the above rule is if a node is boolean Then only the probability for the true state need be given For example if node It_Falls is boolean its equation could be p It _Falls Weight Size Weight Size gt 10 0 10 Weight Size gt 5 0 03 0 01 Differences between standard Java or C C equation syntax The Netica equation syntax is the same as in the Java and C and C programming languages except the part to the left of the assignment operator is different and no semicolon is required at the end of the equation Furthermore the Java C C bitwise operators such as amp are not available in Netica but the logical operators amp amp are In addition Netica has a logical xor function A final difference is that the bitwise xor operator of Java C C is instead used as the power operator by Netica thus 2 3 8 All of the C Standard Library math functions sin log sqrt floor etc are available and use the same names JAVA VERSION 4 18 NETICA API 87 11 3 Equation Conditionals Suppose continuous node X has the parents Y and B If you wanted to give P X Y a different equation involving X and Y for different values of B you could write a conditional statement using the and operators like this p XIY B B lt 2 NormalDist X 3 Y 1 B lt 6 NormalDist X 2 Y 3 UniformDist X 0 10 The conditions are evaluated in order so the fi
12. and use the data within to learn a Bayes net performance test a Bayes net etc First you create a DatabaseManager instance using DatabaseManager String odbcConnectionString String control Environ env JAVA VERSION 4 18 NETICA API 41 The connection string has information on the file location of the database the driver to use depending on whether MySQL MS Access etc any password required to access the database etc as described in the javadocs for the DatabaseManager constructor Now that you have the database manager you can use it to execute whatever SQL commands you would like on the database using void DatabaseManager executeSQL String sqlCmd String control If you wish to put all the findings currently entered into a Bayes net as a new record of the database use void DatabaseManager insertFindings NodeList nodeList String columnNames String tables String control Where ColumnNames is a list of columns in the database table to map to the list of nodes nodeList To use the database with Netica functions such as learning from data you first create an empty Caseset instance and then add the database to it with void Caseset addCases DatabaseManager dbMgr double degree NodeList nodeList String columnNames String tables String condition String control Then the resulting Caseset can be used as described in the Caseset section The previous two functions assumed that the Bayes ne
13. cccccsscessecsteceseceseceeeeeeeeeeeeeees 11 4 Converting an Equation to a Table ee ceeeseeeeeeeeeeees 11 5 Equations and Table Size cc ce ccccesccsseceteceteceeeesteeeeeeeees 116 TemK Names hs ci eitran reai at ade Aaea ER AKEE fees 11 7 Referring to States of Discrete Nodes 0 ceeeeeeeeeeeeees 11 8 Constant Nodes as Adjustable Parameters 00100000000000 11 9 Tips on Using Equations ccccsessecsteceseceseceseeseeeeeeeeees 11 10 Specialized Examples cccccccscesseestecstecesecesecesseeseeeeeeeees 11 11 Equation Constants Operators and Functions 11 12 Special Math and Distribution Functions Reference 12 Bibliography 13 Functions by Category JAVA VERSION 4 18 JAVA VERSION 4 18 NETICA API Node iStS sie scastsnseruttelsaucbedsiggei i pacet aa hasten headed ai haee danse zie aO E E Eni 107 Cases Sets of Findings insosn erren e EA 107 Sensitivity to Findings Utility Free Value of Information 0 0 0 0 eee 108 Performance Testing a Net cccccssccssecsseceseceseceseceeeceeeeseeeeeseeeseeeseeeeeeneeesaees 108 Database Connectivity mesener ane Ea EEE EE AG 108 High Level Net Modification cccccccssccsseceseceseceeeceeeeeeeeeeseesseeeeeenseeseeenaees 108 Low Level Net Modification cccccccccesecsseceseceseceeecseeeeeeeeeseeeseeeeeeeeeseeeaees 109 Retrieving Net Information ccccecsccesecesecsneceseceeeceeeeeeeeeeaeeeseeeseeeeeeneeeneees 109 EQUatlONS
14. for their own net and node classes that inherit from norsys netica Net and norsys netica Node respectively The supplied files in src neticaEx aliases have examples of this Although overloading the terms Net and Node like this is not difficult namespace conflicts may arise In general if you explicitly import your Node or Net class the Java compiler will use those as the default classes 2 3 Multithreading If you are running Netica J within a single process and are not creating more than one thread in that process you don t need to consider this issue However if you are operating in a concurrent usage environment then you need to consider threading issues Netica J is threadsafe in that if one thread calls JAVA VERSION 4 18 NETICA API 17 a Netica J function and while it is executing another thread calls a Netica J function the new call will not interfere even if they are both trying to operate on the same object the new call will execute after the original is done Of course your software must do its own appropriate synchronization and consider race possibilities if you have more than one thread working on the same object such as net or node at the same time Threads operating on separate nets will not have any interference For efficiency reasons you may want to consider the following Many Netica J functions will block other Netica J functions until they return This is an efficiency concern only and
15. i System out print t node state i getName System out printin tActual for inta 0 a lt numStates a for int p 0 p lt numStates p JAVA VERSION 4 18 NETICA API System out print t int nt getConfusion node p a System out println t node state a getName And this is the output it produces Confusion matrix for Cancer present absent Actual 9 2 present 4 185 absent Error rate for Cancer 0 03 Logarithmic loss for Cancer 0 08219048904200114 59 60 NETICA API JAVA VERSION 4 18 7 Modifying Nets A common scenario is that you ve built a Bayes net using Netica Application or Netica API as described in the Building and Saving Nets chapter and saved the file Now your program uses Netica API to read the net file and use it to solve problems Each of the problems is a little bit different and it s not enough to just enter different findings you need to modify the net itself Perhaps it s a small change like altering the CPT tables adding new states to a node changing utilities or converting decision nodes to nature nodes Or maybe it is a major operation like taking several net fragments from different nets and stitching them together to make a new net for the particular problem at hand This chapter discusses some ways to modify a net in place and then in the section Node Libraries it discusses how to create libraries of nodes or n
16. is called with a list of nodes Nodes not present in the list passed will not have their probabilities revised so normally it will be a list of all the nodes in the net Nodes in the list for which the case provides sufficient data will have their probabilities revised a small amount to account for the case and their experience levels increased slightly as well The batch mode way of revising probabilities does exactly the same thing as the one by one way but for a whole file of cases at once You call Net reviseCPTSByCaseFi le with the file and the same list of nodes as before and it does the same thing as the one by one method for each of the cases in the file only much more efficiently than if you were to read in the cases one by one and call Net reviseCPTsSByFindings each time See the Findings and Cases chapter for more information on creating a file of cases If the case file has a node value that doesn t correspond to any state of that node in the net e g the states P y g of net node color are red and green and the value for color in the case file is blue then an error will 52 NETICA API JAVA VERSION 4 18 be generated An exception to this is if one of the states of the net node is called other Then the case will be read without error and the finding for the node will be other 6 5 Example of Counting Learning The program below LearnCPTs java will demonstrate learning from cases This progra
17. k a b Lalli 1 b a 1 Required a lt b k a b are integers This distribution represents the situation where k has an equal probability of taking on any of the integer values from a to b inclusive where a and b are integers If k were continuous then it would be a continuous uniform distribution eqnear reldiff x y X Y max X Y lt reldiff where reldiff 0 Returns TRUE iff x is equal to y within reldiff To use a tiny built in value for rel diff suitable for numerical floating point inaccuracy use approx eq erf x ae exp t dt Va where x is an unrestricted real This returns the error function of x It is useful for calculating integrals of the normal distribution function NormalDist If x is large you can obtain better accuracy with erfc erfc x erf x where x is an unrestricted real This returns the complementary error function of x It is useful for calculating an integral of a tail of a normal distribution function NormalDist It would be easy enough to just use 1 erf x but this provides better numerical accuracy when x is large so erf x is very close to 1 ExponentialDist x A La exp A x Required A gt 0O 98 NETICA API JAVA VERSION 4 18 If events occur by a Poisson process then the time between successive events is described by the exponential distribution where is the average number of events per unit time ExtremeValueDist x a B l exp
18. node Smoking kind NATURE discrete TRUE states smoker parents probs smoker 0 5 he nonsmoker nonsmoker 0 5 The file adheres to the DNET format which is 32 NETICA API Smoking smoker nonsmoker node Cancer kind NATURE discrete TRUE states present absent parents Smoking probs present absent O 1 Os Oy 0 01 0 99 title Lung Cancer e node TbOrCa kind NATURE discrete TRUE states true false parents Tuberculosis Cancer probs true false Tuberculosis 1 0 present 1 0 present 1 0 absent 0 1 absent title Tuberculosis or Cancer node XRay kind NATURE discrete TRUE states abnormal normal parents TbOrCa probs abnormal normal TbOrCa 0 98 0 02 true 0 05 03 95 7 false he e JAVA VERSION 4 18 Cancer present absent present absent The DNET file format is a text format but Netica can also work with a binary format called NETA The binary files are much smaller they usually read faster and Netica can encrypt them To save the above net in NETA format you would change the call to net write to be net write new Streamer Built_ChestClinic neta That is the call is exactly the same as for a DNET file but the file name has an extension of neta instead of anything else The Net
19. setTitle state setComment state setNumeric setLevels addStates state delete reorderStates addLink deleteLink switchParent setInputName addListener Creates a new empty net Frees all memory used by a net and all its substructures Changes the name of the net Changes whether a node does belief updating immediately Provides the elimination order to be used for the next compilation Sets the string used to title a net Attaches a comment string to the net Attaches a callback for when nodes get created removed etc Creates a new node for a given net Removes a node from its net and frees the memory it required Duplicates each node in a list putting them in same or new net Adds to a given net nodes that match the variables in the database Changes the name of a node Sets the string used to title a node Attaches a comment string to the node Changes whether the node is a nature decision utility etc node Names all the states of a node at once with a comma delimited string Provides a name for a state of the node Sets the title ofa state of the node Attaches a comment to the state of a node Sets a real number for a state of a discrete node Sets threshold numbers for continuous discrete conversion Inserts one or more states into a node s list of states Remove a state from a node Changes the order of a node s states Adds a link from one node to another Removes a link from one node to another Switches a link tha
20. 25c3 i seicea E S sate te Soo Sig oceans atv detec avd vee osesarlases Re bASe 110 Tables sis saz hci se ocei cnt Pant advo ces eesti Cab oe eae aie eed ne EE aah eoe ve enka ak E eens 110 INGGE S Cts ett ts th iack ees a betat amis a aa Maat sh A ene 110 Visual Display noria ran ee eh ain ae aehle isha alhee sees 111 User Data 1elds s5 21 235 eves sb toa vadeeeetths toa E A e ENA 111 14 Index 112 6 NETICA API JAVA VERSION 4 18 1 Introduction This reference manual is for Netica J the Java version of the Netica API Programmer s Library It is meant to be used in conjunction with the onscreen Netica J javadocs reference see below Netica J is a set of Java classes and an accompanying Java Native Interface JNI library that allow a Java developer to use the Netica API Programmer s Library for working with Bayesian networks This manual is not a manual for Netica Application which is an easy to use point and click application program with much of the same functionality see http www norsys com netica html Users of the API will typically want to have the Application handy for visually inspecting and modifying nets A version of Netica soon to be released will allow Netica API to use the GUI of Netica Application Besides Java other versions of Netica API exist for C C C and Visual Basic each offering the full Netica functionality Visit http www norsys com netica_api html to learn more about the other members
21. API 79 void Net reorderNodesets String nodesetOrder Re orders the priority of the node sets as requested priority is used to choose display color Any node sets contained in the comma separated string nodesetOrder will become the highest priority with the nodes earlier in that list being higher priority The priority of nodes not mentioned in nodesetOrder will not be modified java awt Color Net getNodesetColor String nodeset void Net setNodesetColor String nodeset java awt Color color 10 2 Graph Algorithms The nodes and links of a Bayes net form a graph as defined in graph theory Graph theory provides algorithms to efficiently find all the descendents of a node or all its ancestors connected nodes Markov blanket etc Netica very efficiently implements these algorithms and makes them available with the Node method void getRelatedNodes NodeList relatedNodes String relation To use it you pass the relation you desire as a string and a node list to be filled Then the function puts all of the related nodes into the list For example to find the Markov blanket of node_A you could use NodeList mb new NodeList net node_A getRelatedNodes mb markov_blanket After execution the list mb will contain all the nodes in the Markov blanket of node_A The allowed relation strings are parents children ancestors descendents connected markov_blanket and d_connected the singular version
22. Bar true 70 0 false 30 0 Pa Labeled Box Text The NodePanel class itself is an abstract base class that manages a number of common functions of all NodePanels such as hooking up to the Netica Node that is represented and discovering it s title or name if it lacks a title managing event listeners and managing display modes hi lighted normal or grayed 9 5 Event Handling Besides being standard JComponents and hence being able to partake of all the standard Java AWT SWING events NetPanel and NodePanel objects are also norsys netica gui RecursingEventListeners The RecursingEventListener interface provides two very convenient methods addListenerToAllComponents java util EventListener eventListener and removeListenerFromAllComponents java util EventListener eventListener These will recursively run through all the subcomponents of the NetPanel or NodePanel and attach the EventListener to those subcomponents Thus with a single command you can add an event listener to all the components within a NetPanel 9 6 NetViewer Included in the examples directory of this distribution is a reasonably sophisticated program NetViewer java This program allows you to select a net from a list whereupon it draws the selected net and then allows you to edit the net and to enter finding information as well It illustrates how to attach mouse events to nodes to parts of nodes e g the belief bars rows and even to links I
23. Caseset Net Net constructor constructor finalize setPassword g setCaseFileDelimChar g setMissingDataChar write constructor writeFindings readFindings writeCases addCases reviseCPTsByCaseFile getFileName Initializes the Netica system Signals an end to using Netica system and frees all possible resources e g memory close any open files Adjusts the amount that Netica functions check their arguments Gets the software version of Netica currently running Adjusts the amount of memory that Netica can allocate for tables The symbol to separate data fields in case files created by Netica The symbol indicating missing data in case files created by Netica Returns an error message for the given error report Indicates the nature of the error out of memory aborted etc Returns the severity level of the given error report Returns the error number of the given error report Adjusts the amount that Netica functions check their arguments Creates a stream for the file with the given name Creates a stream for reading and writing to buffers in memory Closes files frees resources and deletes either type of stream Sets a password to read or write encrypted files The symbol to separate data fields in case files created by Netica The symbol indicating missing data in case files created by Netica Saves a net to a file Reads a net from a file Saves a net s current set of findings to a file Reads findings from a file and
24. Data cecceecceeseeeteeees 56 7 Modifying Nets 60 7 1 Common Modifications nea aaae E E A AE ATR 60 NETICA API TA Node Libraries sess sctes iii auth a A RRE 7 2 Net REqUcthOMscs cesses 3d cevareahtevesesgse ceased cess T EA eriede 7 3 Probabilistic Inference by Node Absorption cccceeeee 8 Decision Nets 8 1 Programming Example ccccesccescessceesceeeceeseeeeeeneeesseenaes 9 Drawing Nodes and Nets 9 1 Netica Net Visual Properties and the gui Package 912 Node Position neren see ov Rea Btes tet tote Sea ahs ob ads 9 3 Node Styler a E e R s 9 4 Drawing Nodes sisniars eteisen a i a a 9 5 Event Handlin giiess i sSs ceasdanseveters dacaigiavetieca ETEA E EN 9 6 Net Vie WET orire E EE a A A AA NES 9 7 Miscellaneous Useful Features ccccccccscccsssceesseceesseeeseees 9 8 Feedback Wantedo asmia eura oma tives eecdecbleoe a aekes 10 Special Topics 10 1 Node Lists and Node sets ccccccsssceescccesseeesseceesseeeseees 10 2 Graph Algorithms ccccsceessecstecsteceteceeceteeseeeeteeseeeeees 10 3 User defined Data ccccccccccccsscceessecesseecsssceessecseseeeeees 104 SSONSItIVIEY cc casies tik es ec occa tovsh cheer a a 10 5 Stochastic Simulation ccccccccccssecesscecesseeeseceesseeessees 11 Equations Lb Simple Example Sie sneri i i 11 2 Equation Syntax ccccccccecsessceeseesecsteceeceseeseeeseeeeeeeeees 11 3 Equation Conditionals
25. Java classes General NeticaEvent NeticaException NeticaListener NodeList State User Util Value and VisualNode do not have peer equivalents The existence of peer relationships is usually transparent to the Java developer Netica J was designed to give the developer as much as possible the sense he she is working in a 100 pure Java environment That provides the best of both worlds the productivity safety and memory management of Java with the speed and reliability of a highly optimized highly tested widely used native binary 18 NETICA API JAVA VERSION 4 18 The only situations where you need to know about peer objects is when considering finalization and the cleanup of native resources discussed in the Finalizers section below or when working in a model view controller MVC environment where things could be happening to the native model objects and the Java environment is presenting but one view on that model This can happen for instance if Netica J is communicating with peer objects inside Netica Application A user of Netica Application could delete a native node via the GUI and the Java environment would then find that its Node object had been disconnected from its peer Netica J has a standard Java Publish and Subscribe mechanism using NeticaEventListeners for Java objects to be made aware of such occurrences on the native side of the universe see the Event Handling section below 2 6 Exception Handling Ex
26. New versions of Netica API are available for download from the Norsys website from the Downloads menu at www norsys com If you are using a license password it will work with any version released within a year of the password being issued and often longer If you would like to be notified of version updates and other news regarding Netica J please visit https www norsys com mailing list html interests Netica J and supply us with your e mail address Mailings are infrequent and your privacy will be respected We at Norsys have worked hard to make Netica J a very high quality and robust package that is easy and natural to use If you have any ideas for how it can be improved we would be very happy to hear them Please send your suggestions to netica j norsys com 14 NETICA API JAVA VERSION 4 18 1 7 Other Resources The following resources at the Norsys website may be helpful when using Netica API Netica Application This program has an easy to use graphical interface and most developers working with Netica API use it to visualize and or edit the Bayes nets they are working with It is also useful for experimentation and trying out concepts that are to be implemented using Netica API since it operates in much the same way Website location http www norsys com netica html Resources Page Describes training consulting literature and websites available for Netica Website location http www no
27. Node g setEquation Node equationToTable Node g setInputName Node calcState Node calcValue Tables Node g setCPTable Node g setExperTable Node g setStateFuncTable Node g setRealFuncTable Node deleteTables Node hasTable Node isDeterministic NodeList mapStateList Node equationToTable Learner learnCPTs Net reviseCPTsByFindings Net reviseCPTsByCaseFile Node fadeCPTable Node Sets Node addToNodeset Node removeFromNodeset NETICA API JAVA VERSION 4 18 Returns a comment string for the node Returns whether the node is for a discrete or continuous variable Returns whether the node is a nature decision utility etc node Returns the number of states node can take on Returns the name of the given state Returns the state number of the state with the given name Returns the title of the given state Returns the comment of the given state Returns the real number associated with a state of a discrete node Returns threshold numbers for continuous discrete conversion Returns the parent index of the link with the given name Returns a node list of the parents of the node Returns a node list of the children of the node Checks if a node has a given graphical relationship such as D connected Markov blanket ancestors children etc with another node Finds all the nodes that bear a given relationship with a given node Finds the nodes that bear a given relationship with a given set of nodes Set a node s equation expressing the n
28. Programming Example Below is a listing of the program MakeDecision java which build this decision net in memory and then solves it i e finds the optimal decisions This program can be found in the examples directory of your Netica C distribution Much of it is very similar to building a Bayes net see the chapter Building and Saving Nets for explanations of those parts We will discuss the things new to this example When a node is first created with new Node it starts off as a nature node Here we change Umbrella into a decision node and Satisfaction into a utility node using Node setKind Node is passed the number of states of the node and in this example as well as having 2 state nodes there is also a 3 state node and a continuous node indicated by passing 0 for number of states Utility nodes are always continuous deterministic nodes We use Node setRealFuncTable to build up the relations of a deterministic node instead of Node setCPTable but it works in a similar fashion r MakeDecision java Example use of Netica J to build a decision net and choose an optimal decision with it import norsys netica import norsys neticaEx aliases Node public class MakeDecision public static void main String args try Node setConstructorClass norsys neticaEx aliases Node Environ env new Environ null Net net new Net JAVA VERSION 4 18 NETICA API 69 Node weather new Node We
29. String relation NodeList ofNodes Sometimes you don t need a list of all the nodes bearing some relation to a certain node you just want to know if that relation holds between two nodes For example you may want to know if node A is an ancestor of node B You could use the function described above to generate the whole list of ancestors of B and then check if A is a member but that would be wasteful Instead you call Node isRelatedQ like this if node_A isRelated ancestor node_B 10 3 User defined Data Sometimes it is very useful to be able to attach your own data to Netica objects Netica doesn t do anything with that data it just holds the data until you ask for it back The Netica objects that you can attach data to are nets Net and nodes Node There are two different ways of attaching data One is to attach to the Netica object a single Java object That object can be whatever you wish perhaps a large collection When the Netica object is duplicated or saved to file the reference you have attached will be ignored Only one such arbitrary Java object can be attached to each Netica object The relevant methods for attaching and retrieving data in this way are Node Net Environ user setReference and Node Net Environ user getReferenceQ void setReference Object obj Object getReference The other way of attaching data to Netica objects is by user fields with which you can attach as many data i
30. can It can be used whenever there is not much missing data or uncertain findings for the learning nodes or their parents When learning the CPT of a node by counting Netica will only use those cases which supply values of certainty for the node and all of its parents Obviously if any of those are latent nodes counting will not work If you can t use counting then you must use EM learning or gradient descent For each application area it is usually best to try each one to see which gives the better results Generally speaking EM learning is more robust i e gives good results in wide variety of situations but sometimes gradient descent is faster For all three algorithms the order of the cases doesn t matter 48 NETICA API JAVA VERSION 4 18 During Bayes net learning we are trying to find the maximum likelihood Bayes net which is the net that is the most likely given the data If N is the net and D is the data we are looking for the N which gives the highest P N D Using Bayes rule P N D P DIN P N P D Since P D will be the same for all the candidate nets we are trying to maximize P D N P N which is the same as maximizing its logarithm log P D N log P N Below we consider each of the two terms of this equation The more data you have the more important the first term will be compared to the second There are different approaches to dealing with the second term log P N which is the prior probability of
31. dash and then the name of the node Continuing with the above example if a new node Switch could take on the values 0 1 and 2 you could write Color Switch selectO Switch red Color yellow blue The Color was not required on yellow and blue because the context was carried over from red Color but it could be put there as well If a discrete node has a numeric value associated with each state see Node setLevels that numeric value can be used in an equation instead of the state name 90 NETICA API JAVA VERSION 4 18 Alternatively you can use the state index numbering starts at 0 preceded by a hash character However it is recommended to use the names or values because they are more readable less error prone and more robust to future changes to the node such as the adding or re ordering of states 11 8 Constant Nodes as Adjustable Parameters Sometimes it is useful to have an equation parameter that normally acts as a fixed constant but which you can change from time to time That is the purpose of a constant node You create a constant node by addinga nature node to the network and then converting it to a constant node by calling Node setKind You can also set other characteristics of a constant node in the same way as any other node such as giving it state names To set or change the value of a constant node enter the value in the same way as you would enter a finding Yo
32. depend on the findings You may just be able to look up the desired probabilities without doing belief updating at all There is a danger to keep in mind Even though the reduced net has fewer nodes than the original it may actually be more complex if many links were added by Net absorbNodes or Node reverseLink remember that the size of a node s conditional probability table can be exponential in its number of parents Generally speaking absorbing out context nodes i e nodes with findings entered which have many ancestor nodes results in the worst increase in complexity The next worst is absorbing out non context nodes i e nodes with no findings which have many descendant nodes Absorbing out context nodes with no ancestors or non context nodes with no descendants will not add any links Of course if the number of target and findings nodes is very small the resulting net must be simpler although the transformations to generate it might temporarily require a lot of memory 7 3 Probabilistic Inference by Node Absorption From the previous section you may have realized it is possible to do probabilistic inference using node absorption by entering all the findings and then absorbing all the nodes except for a single target node The resulting probability distribution for that node can be obtained with Node getCPTable and it will be a single belief vector because the node won t have any parents that is the same as the belief ve
33. exp x a B x a B B Required P gt 0 This distribution is the limiting distribution for the smallest or largest values in large samples drawn from a variety of distributions including the normal distribution Also known as the Fisher Tippet distribution Fisher Tippet Type I distribution or the log Weibull distribution FDist x Vi V2 La Required v gt 0 v gt 0 The ratio of two chi squared variates X and X each divided by their degrees of freedom Xj v1 X2 v2 follows an F distribution Also known as Snedecor s F distribution Fisher Snedecor distribution F ratio distribution and variance ratio distribution factorial n n n 1 n 2 1 where n20 n is an integer Returns the factorial of n which is the product of the first n integers factorial n is often written as n factorial 0 1 Even fairly small values of n around 170 can cause factorial to overflow For that reason calculations with the factorial function are often done using the logarithm of the results for which you can use logfactorial If n is not an integer you may want to use the gamma function which for integer values is related to factorial by factorial n gamma n 1 _ but which is also defined for non integer values gamma x where x20 Returns the gamma function of x The gamma function is normally defined for negative values of x as well but Netica cannot compute these Don t confuse this function with GammaDist
34. for a new case i e it is easy to find the posterior beta function given the prior one and the case In fact that is what the simple equation at the end of this section does At each node Netica stores one experience number for each possible configuration of states of the parent nodes and with it a vector of probabilities one probability for each state of the node The experience level corresponds roughly to the number of cases that have been seen normally it is 1 more than the number of cases This experience has sometimes been called the estimated sample size or ess To save space Netica doesn t store experience numbers for nodes that haven t been involved in any learning and haven t had a manual entry of experience 6 3 Counting Learning Before learning begins providing there has been no previous learning or entry of probabilities by an expert the net starts off in a state of ignorance All probabilities start as uniform and experience starts off as the number of states of the node which is like a single 1 in each unnormalized CPT cell If you would rather that it started from some different value then you can use Node setExperTable to initialize the experience values before learning starts but then you must also initialize the CPTs to uniform A different way is to apply a simple correction at the end of the learning which does the same as Netica Application s Table Harden function For each case to be learne
35. for learning 48 test cases 56 test data See also test cases test nodes 56 test finding best 82 testing performance of net 56 TestNet java file 10 testWithCaseset NetTester 56 in use 57 threadsafe 7 titles 29 trademark notices 2 training cases 46 56 training data See also training cases triangular distribution eqn function 103 Triangular3 Dist eqn function 103 TriangularDist eqn function 103 TriangularEnd3Dist eqn function 103 U Umbrella example 67 unbounded interval in UVF file 43 45 uncertain findings in case file 42 uncertainty 49 Unicode 29 uniform distribution eqn function 97 103 UniformDist eqn function 103 union passed to getRelatedNodes 79 unobserved nodes 56 upgrades website 13 upgrading Netica API 9 user class 80 User class 111 user data fields functions available 111 user defined data 80 user defined fields 80 JAVA VERSION 4 18 UTF 16 29 utility node 67 UVF file 42 complete uncertainty 45 Gaussian 42 interval 43 likelihood 44 negative likelihood 45 set of impossibilities 44 set of possibilities 43 unbounded interval 43 45 V Value class 106 value node 67 value of information utility free functions available 108 variable 21 variance due to findings 82 variance ratio distribution eqn function 98 varying node 82 version number of license 9 vir
36. index 1 if argmin1 is used At least one argument must be passed See also min argmax select Example argminO 10 6 6 3 4 126 3 4 returns 2 argminl 10 6 6 3 4 126 3 4 returns 3 BernoulliDist b p llh b p l p Required 0 lt p lt 1 b boolean This is the distribution for a single Bernoulli trial in which p is the probability of an outcome labeled success occurring b is a boolean that is true if the success occurs An example is flipping a coin and checking for the event of heads appearing _BernoulliDist This is a distribution that Netica uses internally to represent the Bernoulli distribution BernoulliDist Ifyou get an error message saying there was an error evaluating _Bernoulli k p where k and p are numbers then your equation is supplying illegal values even if you never explicitly used _Bernoulli in your equation For instance if your equation for boolean B is P B x x 10 and values of x can go up to 11 then _Bernoulli 1 1 1 will be illegal since you are supplying 1 1 as a probability and Netica can t normalize it since no probability for B being false is given beta z w gamma z gamma w gamma z w where z gt 0 w gt 0 Returns the beta function of z and w BetaDist is the beta probability distribution which is based on the beta function BetaDist x a La x 1 x beta a B Required a gt 0 B gt 0 The beta distribution over x Almost any reasonably sm
37. javadocs You can see that the entire program is wrapped within single try catch block Most Netica J API methods throw NeticaException exceptions if anything erroneous is attempted or results Next net compile builds the junction tree of cliques and attaches it to the data structure of the Bayes net but does not discard any of the information from the original Bayes net We can now use this net to diagnose a new patient who has just entered the clinic In the next line Node getBeliefQ is called to determine the probability tuberculosis is present double belief tuberculosis getBelief present JAVA VERSION 4 18 NETICA API 25 This causes a belief updating to be done which finds new beliefs for all the nodes in the net This step can be time consuming if the net is very large or highly connected If Node getBelief is then called for some other node it would return almost immediately because the calculated beliefs have been saved at each node The program then prints out the probability of tuberculosis which we can see is 1 04 from the listing of the program output below This is the probability that the new patient has tuberculosis before we know anything else about him The number may seem high but then perhaps this net was built for people entering a certain clinic and many of them wouldn t be there unless they have some kind of illness An X ray is taken of the patient and it comes out abnormal A Bayes n
38. multinomial eqn function 100 multinomial distribution eqn function 100 MultinomialDist eqn function 100 multiplicity of cases 37 multithreading 7 17 mutual information 82 mutually exclusive 29 MySQL database 40 N NAME MAX General 29 names 29 native objects and code 17 nature node 67 nearest0 eqn function 100 nearest eqn function 100 negative binomial distribution eqn function 101 negative finding 34 negative likelihood in UVF file 45 NegBinomialDist eqn function 101 Net class 106 108 109 net library 14 net reduction 64 Net constructor 24 29 for new library 62 in use 23 62 68 in use to read file 63 Net java file 10 NETA file format 32 NetEx java file 10 16 Netica API 6 Netica Application 6 14 27 transferring info 81 website 14 Netica dll 10 NeticaError class 105 NeticaEx 15 JAVA VERSION 4 18 NeticaException class 18 Netica J 6 NeticaJ dll 10 NeticaJ jar 10 NeticaJ_Man pdf file 10 NetPanel constructor in use 72 NetTester class 108 NetTester constructor 56 in use 57 NetTester java example program 57 NetViewer java file 10 neural networks 49 NEXT_CASE in use 52 NO_MORE CASES in use 52 node 21 node absorption 64 65 Node class 109 110 node library example program 62 node library 61 node lists 77 functions available 107 Node constructor 29 60 in use 6
39. mutual information is the only function that can be used If the target node is a discretized continuous node or a discrete node with a real number associated with each state then the variance of real measure is the recommended measure although you may wish to use mutual information in some situations The mutual information is the reduction in entropy of the target node belief distribution due to a finding at the varying node over each possible finding weighted by the probability of obtaining that finding When you call one of the two functions it will return the sensitivity of the original targetNode used in the construction of the Sensitivity with respect to the varyingNode passed in The first time it is called it takes longer to return since it is calculating the results for all the varyingNodes that were used in the construction of the Sensitivity because it can save time doing them all at once but it remembers the results so subsequent calls are very fast unless a finding or something else in the net changes in which case it must re calculate Mutual information is symmetric i e it has the same value when the target node and varying node are reversed so you can use getMutualInfo to efficiently determine how much obtaining a finding at one node will likely effect the beliefs of all the rest of the nodes in the net When you are finished using a Sensitivity object you can safely free its resources using finalize
40. new Environ null DrawNet dn new DrawNet args 0 catch Exception e e printStackTrace You call the program with java DrawNet SomeNet dne or neta and it will draw the net in a fashion similar to the way that Netica Application does with the nature nodes drawn using the popular belief bar style If you d prefer a different style then simply replace NodePanel NODE_STYLE_AUTO_SELECT in the NetPanel constructor call with the style of your choice Here is the window that the command java DrawNet Data Files ChestClinic WithVisuals dne creates Visit To Asia Smoker 50 0 NonSmoker 50 0 Present 5 5 ea Absent 94 5 True 6 5 JERN False 93 5 Present 10 0 Maybe 10 0 Absent 80 0 Visit 1 0 ET No_Visit 99 0 Present 1 0 Tr Present Absent 99 0 Absent Chest Clinic XRay Result Abnormal 11 0 EE Normal 89 0 74 NETICA API JAVA VERSION 4 18 9 1 Netica Net Visual Properties and the gui Package Netica files dne and neta files may optionally contain visual information as to the size position and visual style of the nodes they contain This visual information is used both by the Netica Application and the Netica J gui package in order to help decide where and how to display the net components The general policy of a Netica graphical application is to attempt to make sense of and employ the visual information that is present bu
41. norsys com netica html for details to purchase or to download a size restricted free version With the exception of norsys netica VisualNode all of the classes relevant to graphical display can be found in the norsys netica gui package The two most important classes in this package are NodePanel and NetPanel Each of these is a javax swing JPanel that displays assorted graphical components e g JLabels within itself You typically have full access to these subcomponents and so can change colors fonts and borders attach event listeners set visibility etc just as you would with any AWT SWING component The philosophy behind the development of the gui package is to enable you to very easily and rapidly add graphical displays to your Netica J programs For instance the following tiny program is all that is needed to display a net import norsys netica import norsys netica gui import javax swing class DrawNet extends JFrame public DrawNet String netName throws Exception Net net new Net new Streamer netName net compile optional NetPanel netPanel new NetPanel net NodePanel NODE_STYLE_AUTO_SELECT getContentPane add new JScrollPane netPanel adds the NetPanel to ourself setDefaultCloseOperation JFrame EXIT_ON_CLOSE setSize 800 500 or supply getPreferredSize JAVA VERSION 4 18 NETICA API 73 show public static void main String args try Environ env
42. other languages e Efficient Is optimized for speed and is not too large 2 MB typical e Many Platforms Is available for a wide range of platforms including MS Windows 95 NT to Vista Linux Macintosh AIX etc Contact Norsys for other platforms JAVA VERSION 4 18 NETICA API 9 Memory Limiting You can set a bound on how much total heap space Netica J API is allowed to allocate for large tables thereby preventing virtual memory thrashing or the memory starving of other parts of your application e Java Oriented Features e Clean object oriented design e Comprehensive javadocs and manual e Sample java source applications to get you started e Uses Java s exception handling mechanism in the natural way e Supports event listening by any Java object for events such as the creation deletion duplication etc of Nets or Nodes e Supports user data fields for any Serializable Java object e Supports standard Java I O streams e Supplies graphical visualization of Bayes nets with AWT SWING classes e More Features A more extensive list of features is available from http www norsys com netica_api html 1 2 License Agreement and Password Before using Netica API make sure you accept the license agreement that is included in this package as the file License Agreement pdf If you have purchased a license to use Netica API you will have received a license password by email on the invoice and or on the shipped disk You pass the
43. probabilities being the probabilities before any findings were entered Probabilistic inference done within a Bayes net is called belief updating Probabilistic inference only results in a set of beliefs at each node it does not change the net knowledge base at all If the findings that have been entered are a true example that might give some indication of cases which will be seen in the future you may think that they should change the knowledge base a little bit as well so that next time it is used its conditional probabilities more accurately reflect the real world To achieve this you would also do probability revision which is described in the Learning From Case Data chapter As well as regular probabilistic inference Netica can do a number of other types of inference such as finding the most probable explanation MPE finding mutual information solving decision nets node absorption etc 3 2 Netica s Probabilistic Inference There are three ways that Netica can do regular probabilistic inference by junction tree compiling by node absorptions and by sampling For most applications you will want to use the junction tree method because usually it is most convenient and executes much faster You may want to use node absorptions when you have some findings that are going to be repeated in many inferences e g if you discover that something is always true in the context of interest or large parts of a network that are irrelevant t
44. that is indicated by the boolean node Travel The equation below works even though nodes Source and Dest have different sets of states and in a different order Travel Source Dest Source Dest Additive Noise Say you want to represent something like xl x2 gauss 0 0 2 which could indicate that x1 is the same as x2 but with the addition of gaussian noise having mean 0 and s 0 2 You could do this by defining a new node x3 and setting the equations of x1 and x3 as X2 X3 p X3 NormalDist X3 0 0 2 Multiple Discretizations Sometimes it is beneficial to use more than one node to represent a single continuous variable but with each discretized differently For example the more course one may be a parent for another node whose CPT would be too big with a finer discretization while the finer one would serve as a parent for nodes requiring more accuracy Put a link from the finer node to the courser and give the courser node an equation like X5 X20 X20 Noisy Or To create a noisy or node just create a regular boolean nature node put links to it from the possible causes give it a noisy or equation and use that to build its CPT For example if C1 C2 and C3 are boolean nodes representing causes of boolean node E and there are links from each Ci to E then E could have the noisy or equation P E Cl E2563 NoisyOrDist E 0 Clp Os Ba C25 Orar Car 0 1 For its meaning see the NoisyOrD
45. the gamma probability distribution Even fairly small values of x around 170 can cause gamma to overflow For that reason calculations with the gamma function are often done using the logarithm of the results for which you can use Lloggamma For integer values of x the gamma function is related to the factorial function by factorial n gamma n 1 GammaDist x a La x e gamma a B Required a gt 0 B gt 0 If events occur by a Poisson process then the time required for the occurrence of events is described by the gamma distribution where f is the average time between events For a 1 this is the exponential distribution ExponentialDist witha 1 B For B 2 this is the chi square distribution ChiSquareDist with degrees of freedom v 2 a GeometricDist k p lalli p 1 p Required 0 lt p lt 1 k is an integer This distribution describes the number of Bernoulli trials independent trials with outcomes labeled success or failure and constant probability p of success before the first success occurs i e includes only the failure trials An example would be the number of coin flips resulting in tails before the first head is seen JAVA VERSION 4 18 NETICA API 99 Situations where Bernoulli trials are repeated until the nth success are called negative binomial experiments and the geometric distribution is a special case of the negative binomial distribution NegBinomialDist w
46. to be changed based on frequency data that is calculated externally Or perhaps the utility tables of utility nodes are modified based on preference information about a particular end user and then new optimal decisions found The most common change to CPT tables is to adjust them to take into account case data from the world and that is covered in detail in the Learning From Case Data chapter Tables may be changed with Node setCPTableQ Node setStateFuncTableQ Node setRealFuncTableQ Node equationToTable and Node deleteTables An advanced program may wish to lay out the visual positions of all the nodes so that when the Bayes net file is read by Netica Application they will be displayed in the desired layout Or perhaps choose in which style to display each node e g Belief Bars Labeled Box or Hidden The functions to use are Node visual setPosition and Node visual setStyle 7 1 Node Libraries Often the probabilistic relation between a node and its parents represents a small piece of local knowledge which may be applicable in a number of different nets to be used in different situations That relation may have been learned from data or entered by an expert Each new net it is placed in captures the global relations between such local pieces of knowledge and belief updating combines the local and global knowledge with the details of some particular case For example suppose that you made a simple net consisting o
47. updating see Node calcValue and Node CalcState Having this phase increases both accuracy and speed and can be useful for preprocessing input data Another time Netica uses an equation directly is during stochastic simulation calling Node generateRandomCase with method FORWARD_SAMPLING 11 1 Simple Examples Here are some examples of using equations in Netica Suppose X is a continuous variable representing the position of a moving object and is dependent on its parent nodes Velocity Time and Start position This equation could compactly express their relationship X Velocity Time Start Start Velocity Time Now suppose that the start position is zero but that there is some uncertainty about the end position given by the normal distribution with standard deviation S JAVA VERSION 4 18 NETICA API 85 p X Velocity Time S NormalDist X Velocity Time S Here is an example of a discrete node Color with states red blue and green As a parent it has the discrete node Taste with states sour salty and sweet The below is a deterministic equation giving Color as a function of Taste which demonstrates the use of the conditional operator Color Taste Taste sour blue Taste sweet red Taste salty green gray Finally consider a discrete node Color which is indicator taking on the values red or blue depending on whether the parent node Taste is sweet or not but that works imperfectly
48. way of using the GUI to define sets of nodes give them a color and do operations on a whole set at once It displays each node with the color of its node set since a node may be a member of several node sets they have a priority order for determining color and all the node set information is saved in the file with the net Since Netica J works with the net files node sets provide a convenient way to pass sets of nodes back and forth between Netica Application and Netica J Depending on their name some of the sets have special meaning to Netica others have meaning only to the developer NodeLi sts have the following constructor copy constructor access function and finalizer NodeList NodeList Net parentNet Constructs an empty NodeList initial capacity is 100 NodeList NodeList nodeList Copy constructs a new NodeList from an existing NodeList The list is duplicated but not the nodes themselves Node NodeList getNode int index Returns the Nth node of a list the first node is numbered 0 void NodeList finalize Frees the memory used by a list of nodes Not necessary to call since Java will do it automatically 78 NETICA API JAVA VERSION 4 18 As well they inherit the usual functions from java s Vector void NodeList add int index Node element Node NodeList remove int index Node NodeList set int index Node element int NodeList indexOf Node elem int index int NodeList size void NodeList clear H
49. 0 parentStates 1 1 present absent probs 0 1 0 probs 1 0 0 tbOrCa setCPTable parent_states probs There is an even faster way to set the whole CPT table with one function call You call Node setCPTable double cptTable the whole table for the probability array The table you pass in should be in row major form with the last parent varying fastest the same order the table is displayed in the CPT editor of Netica Application If you wish to give a node a deterministic relationship rather than probabilistic you may use Node setStateFuncTable JAVA VERSION 4 18 Now the net is fully constructed in memory and we could use it for inference do net transforms etc but in this example we just save it to a file for later use by calling Net write The resulting file is a pure ASCII text file which can be read back by Netica API or by Netica Application whether they are running on the same computer or another type of computer described in the document DNET File Format It will look similar to the below gt DNET 1 gt bnet Built _ChestClinic node VisitAsia NETICA API kind NATURE discrete TRUE states visit no visit parents probs visit no visit 0 01 0 99 node Tuberculosis kind NATURE discrete TRUE states present absent parents VisitAsia probs present absent VisitAsia 0 05 0 95 visit 0 01 0 99 no visit
50. 0 01 0 99 TbOrCa abnormal normal xRay setCPTable true 0 98 0 02 xRay setCPTable false 0 05 0 95 JAVA VERSION 4 18 NETICA API 29 tbOrCa setEquation TbOrCa Tuberculosis Cancer Tuberculosis Cancer tbOrCa equationToTable 1 false false Streamer stream new Streamer Data Files ChestClinicBuilt dne net write stream net finalize II free resources immediately and safely catch Exception e e printStackTrace First the above program constructs a new empty net with new Net and then adds each of the nodes with new Node Each node represents some scalar variable of interest either discrete or continuous The first string passed to the Node constructor is the name of the node and the second is a comma delimited list of state names for that node The states must be mutually exclusive value can t be two different states at the same time and exhaustive it is always in one of the states Sometimes it is easiest to satisfy the exhaustive condition by having a state called other The names of the net nodes and states are passed as Strings These strings must meet the requirements of an Dname which are The name must be between and General NAME_MAX 30 characters long inclusive The name must consist entirely of alphabetic characters a z and A Z digits and underscores _ The name must start with an alphabetic character e Often they must be un
51. 14 docs directory 11 Dolnference java example program 23 DolInference java file 10 double exponential eqn function 99 Drawing Balls example 49 drawing nodes and nets 72 DrawNet java example program 72 DrawNet java file 10 duplicate 62 duplication of node callback 18 dynamic Bayes nets 7 E Eclipse development system 12 efficiency 22 elimination order 22 EM learning 54 algorithm 49 when to use 47 EM_LEARNING in use 54 email address 6 embedded systems 7 encrypting Bayes net 32 entering findings 35 enterLikelihood Node Value in use 35 enterState Node Value 25 in use 23 35 enterStateNot Node Value in use 35 Environ class 105 Environ constructor 9 24 in use 23 eqnear eqn function 97 equation 84 built in constants 92 built in functions 92 built in operators 92 comparison with Java C 86 conditional statements 87 constant node as parameter 90 deterministic 85 examples 84 91 input names 89 left hand side 85 link names 89 probabilistic 85 referring to discrete states 89 right hand side 86 syntax 85 tips 90 using to build table 88 equations functions available 110 equationToTable 84 88 erf eqn function 97 erfc eqn function 97 error handling NETICA API JAVA VERSION 4 18 functions available 105 error rate 57 ERROR ERR 18 ess 50 estimated sample size 50 event handling 17
52. 2 68 Node java file 10 etPosition Node VisualNode 61 setStyle Node VisualNode 61 NodeEx java file 10 NodeEx java file 16 NodeList class 107 Nodelist java file 10 NodeListEx java file 10 16 NodePanel class 72 node set functions 110 node sets functions available 110 noisy and distribution eqn function 101 NoisyAndDist eqn function 101 noisy max distribution eqn function 101 NoisyMaxDist eqn function 101 noisy or distribution eqn function 101 NoisyOrDist eqn function 101 noisy sum distribution eqn function 101 NoisySumDist eqn function 101 normal distribution eqn function 102 NormalDist eqn function 102 Norsys address 2 NumCases column in case file 37 n o old versions of Netica J 11 optimal decisions 67 Oracle database 40 other state reading case 37 NETICA API 117 P parameter learning 46 parent nodes 21 parents found by getRelatedNodes 79 Pareto distribution eqn function 102 ParetoDist eqn function 102 Pascal 6 performance testing 56 performance testing a net functions available 108 Perl 6 platforms 7 Poisson distribution eqn function 102 Poisson process 98 PoissonDist eqn function 102 positive finding 34 posterior probabilities 21 prediction 7 46 preference utilities 61 preprocessing input data 84 printConfusionMatrix in use 57 prior probabilities 21 probabilis
53. 45 A absorbNodes Net 65 Access Microsoft 40 accuracy of net 56 adaptive learning 55 addCases Caseset 37 40 41 in use 41 57 addLink Node 30 60 in use 62 68 addListener Net and Node 17 addNodes DatabaseManager 41 address of Norsys 2 addStates Node 60 agent modeling 60 ancestor nodes found by getRelatedNodes 79 announcement list 13 append passed to getRelatedNodes 79 approx_eq eqn function 95 arc See also link argmax0 eqn function 95 argmax1 eqn function 95 argmin0 eqn function 96 argmin eqn function 96 asterisk 37 attribute value 37 NETICA API JAVA VERSION 4 18 auto updating 35 B Bayes net 6 adaptive 55 learning 46 Bayes net libraries 61 Bayes net online library 14 27 Bayesian network 6 20 BBN 20 belief 21 belief functions 49 belief network 6 20 belief updating 21 22 25 functions available 106 belief vector 36 Bernoulli distribution eqn function 96 BernoulliDist eqn function 96 beta eqn function 96 beta distribution eqn function 96 beta function 50 Beta4Dist eqn function 96 BetaDist eqn function 96 bin directory 11 binary net files 32 binomial eqn function 96 binomial distribution eqn function 96 binomial experiment 97 BinomialDist eqn function 96 BN 20 BreastCancer cas file 10 BreastCancer dne file 10 bug report email address 13 build
54. N 4 18 special column has the heading NumCases and indicates the frequency or multiplicity of the case A multiplicity of m indicates m cases with the same variable values It is not required to be an integer so it can be used to represent a frequency of occurrence if desired The missing data symbol should not appear in either of these columns if they exist As an example of a case file here is a listing of ChestClinic cas which is produced by the program SimulateCases java listed below and included in the examples directory of your distribution Note that the case file you obtain may be a little different since random numbers are involved It has an IDnum column but no frequency column IDnum VisitAsia Tuberculosis Smo 1 no visit present 2 no visit absent 3 no visit absent 4 no visit absent 5 no visit absent 6 no visit absent 198 no visit absent 200 no visit absent smo smo smo nonsmoker smo smo smo smo king ker ker ker Ker Ker Ker Ker Cancer absent absent present absent present absent absent present TbOrCa true false true false true false false true XRay abnormal normal abnormal normal abnormal abnormal normal abnormal Bronchitis absent presen presen absent presen presen presen presen Here is listing of SimulateCases java the program which generated the above case file g SimulateCases java ee
55. N 4 18 NETICA API 27 4 Building and Saving Nets In the previous chapter we loaded a Bayes net into memory from a file and then did probabilistic inference using it Now we consider how to obtain the net file in the first place Some possibilities are e Obtain a net file of interest from Norsys another company or a colleague by email disk downloading from a website etc The file is machine and operating system independent For examples of Bayes nets see http www norsys com netlibrary index htm e Create the file using a text editor according to the DNET file specification or write a program that creates the DNET text file e Use the Netica Application program to construct the net on the screen of your computer using simple point and click drawing and then save it to a file e Call functions in the Netica API to construct the net in memory Once the net is in memory you may use it for probabilistic inference learning etc or you can save it to a file for later usage In this chapter we will discuss the last method Below is a complete program which constructs the ChestClinic net used in the previous chapter except to be more brief it doesn t include the two nodes Bronchitis and Dyspnea which are not required for the inference examples of that chapter but the code in the examples directory does This program BuildNet java can be found in the examples directory of your Netica J installation r BuildNet java
56. Netica API functions to enter the case as findings into a Bayes net write the case to a file and repeat for each case to be put in the file Case files single case or multi case are pure ASCII text files They may contain gt CASE 1 gt somewhere in the first 3 lines to indicate to Netica what the file contains but that isn t required Then comes a line consisting of headings for the columns Each heading corresponds to one variable of the case and is the name of the node used to represent the variable sometimes the variables are called attributes and the entries in the column values i e attribute value The headings are separated by spaces and or tabs it doesn t matter how many The case data is next with one case per line a single case file would only have one such line The values of the variables are in the same order as the heading line and are separated by spaces or tabs the columns don t have to line up as they do in the example files below The value of a discrete variable is given by its state name or if it doesn t have a state name then by the number symbol followed by its state number e g 3 The state names are preferred since the order of the states may be changed some time and that would render the file invalid The value of a continuous variable is given by a number expressed as an integer decimal or in scientific notation e g 3 21e 7 If the variable has been discretized then the val
57. Netica J Manual Version 4 18 and Higher Java Version of Netica API Norsys Software Corp 2 NETICA API JAVA VERSION 4 18 Netica J Reference Manual Version 4 18 October 21 2010 Copyright 1996 2010 by Norsys Software Corp This document may be copied and stored freely provided it is duplicated in its entirety without modification and including the copyright notice Published by Norsys Software Corp 3512 West 23rd Avenue Vancouver BC CANADA V6S 1K5 www norsys com Netica and Norsys are registered trademarks of Norsys Software Corp Microsoft Windows MS DOS Visual C and Visual Basic are registered trademarks of Microsoft Inc Sun Solaris and Java are registered trademarks of Sun Microsystems Inc Linux is a registered trademark of Linus Torvalds Unicode is a trademark of Unicode Inc PDF is a registered trademark of Adobe Systems Inc X Window System is a trademark of X Consortium Inc IBM and AIX are registered trademarks and PowerPC is a trademark of International Business Machines Corporation Borland is a registered trademark of Borland International Inc Intel and Pentium are registered trademarks of Intel Corporation Hugin is a trademark of Hugin Expert A S Other brands and product names are trademarks of their respective holders While great precaution has been taken in the preparation of this manual we assume no responsibility for errors or omissions Neither is any liability assumed for d
58. Netica dll libnetica a Assuming Netica J was installed at the following location on your filesystem Windows C NeticaJd_325 Unix Linux MacOSX home NeticaJd_ 325 H NeticaJ dll libNeticaJ so jnilib must appear on the java library path Typically this is done with a D option to the JVM For example Windows java Djava library path C NeticaJ_325 bin Unix Linux MacOSX java Djava library path home NeticaJ_ 325 bin 2 NeticaJ jar must appear on the java CLASSPATH For example Windows java classpath C NeticaJ_325 bin NeticaJd jar Unix Linux MacOSX java classpath home NeticaJ_325 bin NeticaJ jar 3 Windows Only Netica dll must appear on the Windows execution path so that Windows can find it For example Windows set PATH C NeticaJ_325 bin PATH Eclipse instructions JAVA VERSION 4 18 NETICA API 13 1 Create your Java project as usual 2 In the Project Properties dialog choose the Java Build Path link then click on the Libraries tab and then click on the Add External Jars link Navigate to the C NeticaJ_325 bin directory and select NeticaJ jar 3 In the Run As dialog go to the Arguments tab and in the VM Arguments window create the following argument Djava library path C NeticaJ_325 bin 4 Windows Only Still in the Run As dialog go to the Environment tab and create a new PATH variable with value C NeticaJ_ 325 bin PATH 1 6 Upgrades Support and Mailing List
59. TRUE say bx then the probability for e is py Ifmore possible causes are TRUE P e will be greater And if leak is nonzero P e will be greater Reducing a p always results in the same or lower P e p can be considered the strength of the relation between e and b with zero indicating independence link could be removed and 1 indicating maximum effect See Pearl88 page 184 for more information his q 1 p i SeealsoNoisyAndDist Example P Effect Causel Cause2 NoisyOrDist Effect 0 1 Causel 0 2 Cause2 0 4 102 NETICA API JAVA VERSION 4 18 NormalDist x p o MA 1 o sqrt 2m exp x p o 2 Required o gt 0 The normal Gaussian distribution of mean p and standard deviation The normal distribution or approximations of it arise frequently in nature this is partly explained by the central limit theorem Since it also has many convenient mathematical properties it is the most commonly used continuous distribution For this distribution 68 2 of the probability is within 1 standard deviation of the mean 95 4 is within 2 standard deviations and 99 74 is within 3 standard deviations If p 0 and o 1 it is known as a standard normal distribution ParetoDist x a b La a b b x a 1 Required a gt 0 b gt 0 The Pareto distribution is a power law probability distribution found in a large number of real world situations such as the distribution of wealth among
60. amages resulting from the use of the information contained herein JAVA VERSION 4 18 NETICA API 3 Contents Jodi ES hh ed oA EERE stich ass caceads cheese ax ceetaceaee ao ed Se wane EEEE EEE 2 1 Introduction 6 1 1 Netica Javac API 3 ccaieei acts scth kad cides pai ati pelea S 6 1 2 License Agreement and Password ccccccescessceseceesceeeeeeeeeeseeeseeeeeeaeensees 9 1 3 Files Ticluded sne oet neie eaten gdh tain nieve tee ned eens 10 VAs Getting Started ss etenn erne naeris eden nanas eaa aT ested aoa anaE S aeiaai 11 1 4 Complete Javadocs Reference ccccssccsseesseestecsteceeceeceeeseecseeeeseeeseeeenes 12 1 5 ADE Installations sin eaii e a e ET R E RE ai 12 1 6 Upgrades Support and Mailing List cc eescsseceteceseceseceeeeeeeeeeeeeeneeeees 13 TP OthersReSOurces 223 s 408ssishcedesceseessadeaes cacesesugeeass E 14 2 Netica J Package Design and Usage 15 2 1 The Ex classes NetEx NodeEx and NodeListEXx cccccccceeseessseceeeee 15 2 2 Inheritance of the Node and Net classes ccccccecsseesseessecsteceeceteeeteeeeenes 16 2 3 Multithreading 2ss0 sdsc0ss1 a rna a e a ead eos leat basen 16 2 4 Event Handlin s s ohe catas nictan lostseehevteste seat cue A E stele ata aes 17 2 5 Java Objects and Native Object Peers c ce cceccccesseeseeseesecseceeeeteeneenes 17 2 6 Exception Handling estes ea ie detads a ieee coded csdetace a aaie aoa 18 2 7 Finalizers amp Memory Management c cccce
61. ant node 90 constant node as parameter in equation 90 context node 64 continuous variable NETICA API 113 in case file 39 undiscretized 22 copyNodes Net in use 62 copyright notice 2 counting learning 47 counting learning algorithm 50 creation of node callback 18 CSV file 36 D d_connected passed to getRelatedNodes 79 database connecting to 40 extracting cases from 40 of cases 36 database connectivity functions available 108 Database Manager class 108 DatabaseManager constructor 40 in use 41 DBNs 7 decision analysis 7 decision net 6 67 solving by node absorption 66 decision nets functions available 107 decision node 67 delete Node 60 delete Node State 60 deleteLink Node 60 deleteTables Node in use 52 deletion of node callback 18 Delphi 6 demo directory 11 Demo program running 11 Demo java file 10 Dempster Shafer 49 dependence degree of 81 finding 79 descendent nodes found by getRelatedNodes 79 deterministic equation 85 deterministic propagation 84 diagnosis 7 46 most informative test 82 directory structure of distro 11 Dirichlet distribution 50 Dirichlet distribution eqn function 100 disclaimer 2 disconnected link 62 discretization avoiding 84 DiscUniformDist eqn function 97 display of nodes 61 DNET file format 14 DNET file 27 31 114 DNET File Format txt file
62. are inconsistent Checking for consistency between the findings of one node and those of another node given the inter node relations encoded in the net is only done if belief updating is done after each finding is entered which will be the case if the net is auto updating see Net setAutoUpdate or if Node getBeliefs is called between entering findings As an example consider the following section of code to enter findings for node which has 4 states a int fst b Node node c float clike belief d float like new float 4 1 like 0 0 6F like 1 0 6F like 2 1 0F like 3 1 0F 2 node finding enterLikelihood like 3 node finding enterStateNot 1 4 like 0 0 5F like 1 0 6F like 2 0 0F like 3 0 5F 5 node finding enterLikelihood like 6 clike node finding getLikelihood 7 node finding enterState 2 8 belief node getBeliefs 9 fst node finding getState 10 node finding clear 11 node finding enterState 2 12 fst node finding getState 13 clike node finding getLikelinood Step 1 sets up a likelihood vector and step 2 enters it as a finding for node The finding means that an observation was made that would certainly be observed if node were in state 2 or 3 and that would occur with probability 0 6 if node were in state 0 or 1 Step 3 enters a negative finding which means the value of node is not sta
63. are known with limited accuracy or only known to within some likelihood In fact Netica has a very elegant practical and powerful way of expressing uncertain findings known as the UVF file format When Netica reads in a case containing uncertain findings for example by Net readFindings it will enter them into the Bayes net as soft findings so any probabilistic inference node absorption sensitivity analysis etc will properly account for them Also the operations on case files such as learning from cases test net with cases and process cases will work properly on case files containing uncertain values When learning from such cases some learning algorithms will work better than others For more information on that and an example of working with case files having uncertain findings see the EM and Gradient Descent Learning section in the next chapter Below is a list of the different types of uncertain findings their syntax in the case file and what they mean Each type of uncertain finding can appear anywhere in a case file where a regular finding normally would For example a UVF file could be a regular case file as described in earlier sections a CSV file or tab delimited text file but with some of the values replaced with entries having the syntax described below Gaussian Syntax m s m and s are real numbers Examples 5 2 3 27 0 03 0 1e 5 JAVA VERSION 4 18 NETICA API 43 This is for a Gaussian a
64. arts structure learning and parameter learning Structure learning determines the dependence and independence of variables and suggests a direction of causation in other words the placement of the links in the net Parameter learning determines the conditional probability table CPT at each node given the link structures and the data Currently Netica only does parameter learning i e you link up the nodes before learning begins However you can use Netica to do structure learning by writing your own small program that tests a number of candidate link structures to find the best one You write a function which searches through some candidate link structures that are plausible and practical in your domain perhaps also adding trial latent variables For each structure you use Netica s parameter learning functions described in this JAVA VERSION 4 18 NETICA API 47 chapter then test the resulting net with Netica s net testing functions also described in this chapter The net that scores the highest perhaps penalized for complexity is the best structure You might not want Netica to learn the CPTs of all the nodes in your Bayes net Some of the nodes may have CPTs that have already been learned well were created manually by an expert or are based on theoretical knowledge of the problem at hand perhaps expressed by an equation Netica allows you to restrict the learning process to a subset of the nodes and those nodes are called the l
65. ass bat for Windows sh for Unix Linux MacOSX e demonstrates building a Bayes net from scratch e demonstrates doing inference e demonstrates creating case instances that statistically derive from a given net e demonstrates learning from cases e demonstrates EM Learning e demonstrates Naive Bayesian Classification of real world medical data e demonstrates building a decision net and choose an optimal decision with it e demonstrates use of the gui package for drawing nets e demonstrates use of the gui package for editing nets and their findings e demonstrates testing the performance of a learned net with the net tester tool e a sample batch file for compiling all the java files in this directory e a sample batch file for running all the java programs in this directory after they have been compiled e an example net file required by SimulateCases LearnCPTs TestNet java e an example net file required by ClassifyData java e a case file created by SimulateCases java and required by TestNet java e ChestClinic dne but including all the size position color display information e a case file required by LearnLatent java e a case file required by ClassifyData java JAVA VERSION 4 18 NETICA API 11 The Netica J directory structure The docs directory contains manuals javadocs license agreements and any other documentation The bin directory contains the Netica J runtime software without which Netica J will not function The sre directory contains so
66. ast one argument must be passed If you just want the index of the maximum i e its position in the list use argmax See also min Example max 10 6 6 3 4 126 3 4 returns 6 6 member elem Si S2 Sn elem s elem s2 elem sn where elemand alls must be the same type Returns TRUE iff one of the s arguments has the same value as elem See also nearest select Examples member 1 6 3 1 3 returns TRUE member C blue red and C red returns TRUE min x1 X2 Xn xj s t x lt xj for all j where x are unrestricted real numbers Returns the minimum of x4 X2 Xn At least one argument must be passed If you just want the index of the minimum i e its position in the list use argmin See also max Example min 10 6 6 3 4 126 3 4 returns 3 4 multinomial ni no Nha n m ny nm ny ny where n20 ni are integers Returns the number of ways an n n2 n sized set of distinct elements can be partitioned into sets of size n n2 Mp If partitioning into only two sets this is the same as binomial MultinomialDist bc n ki pi ko Po Km Pm lil Required n gt 0 k gt 0 O0 lt p lt 1 sump 0 be boolean n k integer The multinomial distribution is a generalization of the binomial distribution to the situation where there are not just two outcomes usually labeled success and fail but rather m outcomes each
67. ated until the log likelihood numbers are no longer improving enough according to a tolerance that you can specify or the desired number of iterations has been reached also a quantity you can specify Netica uses a conjugate gradient descent which performs much better than simple gradient descent To understand how each algorithm works it is best to consult a reference such as Korb amp Nicholson04 Russell amp Norvig95 or Neapolitan04 Briefly EM learning repeatedly takes a Bayes net and uses it to find a better one by doing an expectation E step followed by a maximization M step In the E step it uses regular Bayes net inference with the existing Bayes net to compute the expected value of all the missing data and then the M step finds the maximum likelihood Bayes net given the now extended data i e original data plus expected value of missing data Gradient descent learning searches the space of Bayes net parameters by using the negative log likelihood as an objective function it is trying to minimize Given a Bayes net it can find a better one by using Bayes net inference to calculate the direction of steepest gradient to know how to change the parameters i e CPTs to go in the steepest direction of the gradient i e maximum improvement Actually it uses a much more efficient approach than always JAVA VERSION 4 18 NETICA API 49 taking the steepest path by taking into account its previous path which is why it s called conj
68. ather sunshine rain net Node forecast new Node Forecast sunny cloudy rainy net Node umbrella new Node Umbrella take_umbrella dont_take_umbrella net Node satisfaction new Node Satisfaction 0 net 0 for continuous node umbrella setKind Node DECISION_NODE satisfaction setKind Node UTILITY_NODE forecast addLink weather umbrella addLink forecast satisfaction addLink weather satisfaction addLink umbrella weather setCPTable 0 7 0 3 Il forecast II weather sunny cloudy rainy forecast setCPTable sunshine 0 7 0 2 0 1 forecast setCPTable rain 0 15 0 25 0 6 II weather umbrella utility satisfaction setRealFuncTable sunshine take_umbrella 20 0 satisfaction setRealFuncTable sunshine dont_take_umbrella 100 0 satisfaction setRealFuncTable rain take_umbrella 70 0 satisfaction setRealFuncTable rain dont_take_umbrella 0 0 net compile 1st type of usage To get the expected utilities given the current findings forecast finding enterState sunny float utils umbrella getExpectedUtils returns expected utilities given current findings System out print If the forecast is sunny System out printin the expected utility of umbrella state 0 is utils O ol umbrella state 1 is utils 1 net retractFindings forecast finding enterState cloudy utils umbrella getExpectedUtils
69. because they are more useful in source code form so that you can customize them to your needs Because their Java source is included the Ex classes are a good place to look for coding examples Indeed many of the coding examples found in the javadocs are taken from the Ex classes Unlike the core Netica system the Ex classes may change in future versions methods may be added removed or modified For this reason you may want to keep copies of the Ex classes for future reference or you may want to copy out any methods you need to form your own extensions of the parent classes Since the Ex classes contain so many useful methods many users will want to use the Ex classes in place of the more basic parent classes See Section 3 Inheritance below for considerations when doing this The Ex classes are in part supported by the Netica J user community so please feel welcome to submit additional methods that you have found useful or to suggest improvements to the ones already there 16 NETICA API JAVA VERSION 4 18 Some of the Ex class methods are static while others are not The basic criterion of choosing to make a method static was whether that method could be thought of as a standalone utility that would be useful to have around even when you didn t have an Ex object present Since none of the Ex classes define new state data it is a trivial exercise to convert a static me
70. c static Node duplicate Node oldNode Net newNet throws NeticaException NodeList nodes new NodeList oldNode getNet nodes add oldNode NodeList newNodes newNet copyNodes nodes return newNodes getNode 0 Now the library is constructed and saved to file with instrument as the only node in it At a later session we use the library to construct appnet an application net in which the instrument is used to measure flow and flow2 which are in the same room at the same temperature Net appnet new Net Node flow1 new Node flow1 0 appnet Node flow2 new Node flow2 0 appnet Node rtemp new Node room_temp 0 appnet Node status new Node instrument_status 0 appnet eee 64 NETICA API JAVA VERSION 4 18 Put here Build rest of application net Connect up nodes flow1 flow2 rtemp and status II Add probabilistic relations for flow1 flow2 rtemp and status Hl ie The below will get 2 copies of the instrument node from the library and put them in the application net libnet new Net new Streamer Library dnet Node instrument1 duplicate libnet getNode instrument appnet Node instrument2 duplicate libnet getNode instrument appnet The below will graft them to the other nodes in the application net instrument1 switchParent instrument1 getInputIndex flow_rate flow1 instrument1 switchParent instrument
71. ception handling in Netica J works in the normal Java way If a method encounters an unexpected situation that it cannot resolve a NeticaException is thrown The vast majority of Netica J methods are able to throw a NeticaException The toString method of NeticaException details the reason for the Exception Hence your typical try catch block could look something like this try call Netica J methods catch NeticaException e e printStackTrace If you are familiar with the Netica C API you will find that Netica J s exception handling mechanism makes coding much more convenient and straightforward since you no longer need to actively check if an error has occurred Netica J looks after that for you and will throw a NeticaException automatically if any serious show stopper error occurs By serious we mean any errors of severity level ERROR_ERR or XXX_ERR which means the requested operation was not completed Note that this means that WARNING ERR and lower warnings do not result in a NeticaException being thrown so in those cases where such warnings can occur you can actively call the static method NeticaError getWarnings after the method call to determine if a warning has occurred and if so what the warning was about See the javadocs for NeticaError getWarnings for examples of this It is okay to call NeticaError getWarnings only once in awhile since warnings wi
72. could be p Position Velocity Time Mode 86 NETICA API JAVA VERSION 4 18 Right Hand Side The right hand side of an equation may consist of numbers state names conditionals variables i e parent nodes constant nodes and built in functions constants or operators Probabilistic equations will normally also contain the node the equation is for on the right hand side possibly in several places Nodes Allowed The only nodes which may be mentioned in an equation are the node the equation describes its parents and any constant node Whitespace As many spaces or line breaks as desired may be placed between any two symbols Comments Comments may be embedded in equations and they will be ignored by Netica Everything between and will be interpreted as a comment as will everything between and the end of the line All Values If the equation is for a probabilistic node its right hand side must provide a probability for all the node s possible values so the name of the node must appear there at least once For example if node Color with states red orange yellow has parent Temp with states low med high its equation could be p Color Temp Temp high 2 Color yellow 1 0 0 0 Temp med 2 Color orange 1 0 0 0 Temp low 2 Color orange 0 2 Color red 0 8 0 0 O If you use the built in distributions such as NormalDist the above rule is automatically taken care of
73. csseesseesseeeeeesseesteceeenteesseeees 19 3 Probabilistic Inference 20 3 1 Bayes nets and Probabilistic Inference cccecessceseceseceseceeeceeeeeeeeeseeeenes 20 3 2 Netica s Probabilistic Inference c ce ccccsccesseeesecsteceteceeceeceeceeeesseeeeeeeenes 21 3 3 Example of Probabilistic Inference cccecccssecsseceteceneceseceeeceeeeeneeesneennes 22 4 Building and Saving Nets 27 5 Findings and Cases 34 Del Cases and Case Biless itoe aere eea useeneuetabiases soceesestancesetons 36 5 2 Casesets morina e a tesla a aa a a lp Oe acted NA oe ed aan 40 5 3 Connecting with a Database 0 cccccecsseesseeseeseesseceecesecesecseeseeeeeeeenneennes 40 5 4 Case Files with Uncertain Findings cccscccssccsseceseceseceseceeeceeeeeseeesneenees 42 6 Learning From Case Data 46 6 1 Al Orithims sis as seks At careers nas asic heel a a aie A envenlaweel 47 O22 EXPE ENCE rerea nada oleae ices Lath adhd ss Cea aed a E E ent role Dances 49 6 3 Counting Learin g i ssi onines ade arenar Soara aaen eane esada 50 6 4 How To Do Counting Learning cc ecceceseessecsteceseceeceecesecseeeeseeesneenaes 51 6 5 Example of Counting Learning ccccccccccsseessecsneceneceeceecseecsseeeeneeeneennes 52 6 6 EM and Gradient Descent Learning 0 cceccecceseceteceneceteceeeceeeeeseeesneeenes 54 O57 Ta LE DT EE E A cose edesaghitges Sonadeees tgiegeananeneducneruies ubedbegebsbaaes snes 55 6 8 Performance Testing a Net using Real World
74. ctor that would be obtained by compiling the Bayes net and obtaining the beliefs via belief updating with Node getBeliefsQ The question is which method is faster If you need the beliefs for all the nodes then you would have to repeat the absorbing node method for each of the nodes duplicating the net each time since it is destroyed in the process and so it will usually be far slower But if you only need the beliefs of one node for one set of findings and there are many nodes in the net that are irrelevant to the particular 66 NETICA API JAVA VERSION 4 18 query then the node absorption method can be much faster providing a good elimination order for absorbing the nodes is used It should be mentioned that node absorption will also work with decision nets see the Decision Nets chapter to find optimal decisions When a decision node is absorbed it is not removed from the net instead it is completely disconnected and its decision table set to the optimal decision function When using Net absorbNodes for decision nets the decision nodes must have no forgetting links and if the list of nodes to absorb does not include all the nodes in the net it must consist of a descendant subnet see Shachter86 Shachter88 and Shachter89 for definitions and details of the algorithm used If there are missing no forgetting links or missing descendants in the list of nodes to absorb then Net absorbNodes will absorb as many nodes a
75. d connect to other networks or node configurations e Case Support Can save individual cases i e sets of findings to file and manipulate files of cases Works with the UVF file format which allows cases to be incomplete or have uncertain values Gaussian interval sets of possibilities sets of impossibilities etc and associates an ID number and multiplicity with each case e Simulation Can do sampling i e stochastic simulation to generate random cases with a probability distribution matching the Bayes net Can use a junction tree algorithm for speed or do direct sampling for nets too large to generate CPTs or a junction tree e User Data Every node and network can store by name arbitrary data fields defined by you They may contain numbers strings byte data etc and are saved to file when the object in question is being saved As well there are fields not saved to file which can contain a pointer to anything you wish e Error Handling Has a simple but powerful method for handling usage errors which can generate very detailed error messages if desired e Argument Checking Allows programmers to control how carefully API functions check their arguments when they are called including a development mode to extensively check everything passed to an API function e Compatibility Can work hand in hand with the Netica Application standalone product for example sharing the same files and with Netica API versions for
76. d the following is done Only nodes for which the case supplies a value finding and supplies a value for all its parents have their experience and conditional probabilities JAVA VERSION 4 18 NETICA API 51 modified i e no missing data for that node Each of these nodes are modified as follows Only the single experience number and the single probability vector for the parent configuration which is consistent with the case is modified The new experience number exper is found from the old exper by exper exper degree where degree is the multiplicity of the case passed to the learning routine It is normally 1 but is included so that you can make it 2 to learn two identical cases at once or 1 to unlearn a case etc Within the probability vector the probability for the node state that is consistent with the case is changed from probe to probc as follows probc probe exper degree exper The other probabilities in that vector are changed by prob prob exper exper which will keep the vector normalized exper and exper act as the new and old normalization factors p p p 6 4 How To Do Counting Learning There are two ways to do counting learning from cases singly one by one or in batch mode Here is how you learn from a single case If the case is not already in the Bayes net you enter it into the net as findings see the Findings and Cases chapter Then Net reviseCPTsByFindings
77. decision node of whether or not to take an Umbrella and a utility node that measures our level of Satisfaction There is a link from Weather to Forecast capturing the believed correlation between the two perhaps based on previous observations Umbrella Satisfaction There is a link from Forecast to Umbrella indicating that we will know the forecast when we make the decision It is always the case that links entering a decision node indicate what variables will be known at the time of the decision What we wish to find in solving the decision problem is a function providing the 68 NETICA API JAVA VERSION 4 18 value of the decision node for each possible setting of its parent nodes which maximizes the expected value of the utility nodes In other words we find a contingent plan that tells which decision to make for each possible set of observations that will be made when it is time to act on the decision There is no link from Weather to Umbrella if we knew for certain what the weather was going to be it would be easy to decide whether or not to take the umbrella There are links from Weather and Umbrella to Satisfaction capturing the idea that I am most happy when it is sunny and I don t take my umbrella utility 100 next most when it is raining and I take my umbrella utility 70 I hate carrying my umbrella on a sunny day utility 20 but am most unhappy if it is raining and I don t have one utility 0 8 1
78. demo examples examples Data Files File e NeticaJ_ Man pdf e javadocs e License Agreement pdf e NeticaJ jar e NeticaJ dll libNeticaJ so libNeticaJ jnilib e Netica dll libnetica a n e NetEx java e NodeEx java e NodeListEx java e Net java e Node java e NodeList java e Demo java e compile bat sh e run bat sh e BuildNet java e Dolnference java e SimulateCases java e LearnCPTs java e LearnLatent java e ClassifyData java e MakeDecision java e DrawNet java e NetViewer java e TestNet java e compile bat sh e run bat sh e ChestClinic dne e BreastCancer dne e ChestClinic cas eChestClinic_WithVisuals dne e LearnLatent cas e BreastCancer cas Description e the file for this document e the javadocs directory for Netica J e a legal document relating to the use of Netica API e the Java class library that defines Netica J e the Java to Native interface library Windows only ie 5 iz Unix Linux only i g MacOSX only e the native Netica API library Windows only s MacOSX only e A class containing useful Net methods Node 7 s NodeList e A convenience class that renames NodeEx as Node i NetEx as Net e oe i NodeListEx as NodeList e a sample application to test your Netica J installation e a sample batch file for compiling Demo java bat for Windows sh for Unix Linux MacOSX e a sample batch file for running Demo cl
79. discrete states within a single likelihood vector JAVA VERSION 4 18 NETICA API 45 Scaled Likelihood Syntax S1 Pir S2 P2 Sn Pn each s is a state name state index preceded by interval or unbounded interval Each p is a positive number Some p may be absent Examples red green orange 2 yellow 8 E024 4 2 6 2 This is like a set of impossibilities but with each entry weighted by a number which appears after it If no number appears after it its likelihood is 0 Entries that have numbers above 1 are indicated to be more probable than those not listed and entries with numbers below 1 are less probable than the unlisted ones unlisted entries have a likelihood of 1 Complete Uncertainty Syntax just an asterisk If nothing is known regarding the value of this variable i e missing data then a question mark or an asterisk should be used to indicate that It is equivalent to which is a likelihood of all ones Complete Certainty Syntax v v is a real number state name or state index preceded by Of course any finding of complete certainty may be represented in the usual way which is simply the value it is known to be Likelihood for that value is 1 and for all others 0 46 NETICA API JAVA VERSION 4 18 6 Learning From Case Data Bayes net learning is the process of automatically determining a representative Bayes net given data in the form of cases called the training cas
80. e the method of Net to use is int Net generateRandomCase NodeList nodeList int method double timeout where the method argument determines which algorithm Netica uses for example forward sampling with rejection or by junction tree For an example of a small program using it see the SimulateCases java example program in the Findings and Cases chapter 84 NETICA API JAVA VERSION 4 18 11 Equations The relation between a node and its parent nodes can be defined using an equation if desired This eliminates the burden of building conditional probability tables CPTs manually It is possible to use an equation for continuous or discrete nodes and for probabilistic or deterministic relations Equations are a kind of short hand form of expressing a CPT Since Netica s Bayesian inference usually requires that CPTs be available equations must be converted to tables by calling Node equationToTable before compiling a net or doing certain net transforms like absorbing nodes or reversing links Netica then uses the tables in the same way as if they had been entered directly Sometimes Netica uses an equation directly without the need for a table If findings are entered for all the parents of a node and that node has a deterministic equation then the node is given the exact value computed from the equation which can then propagate to its children during a deterministic propagation phase that is the first step of belief
81. e do so as a likelihood finding A likelihood finding consists of one probability for each state of the node which is the probability that the observation would be made if the node were in that state For our temperature example the likelihood finding would be 0 0 1 1 A common mistake is to think that the likelihood is the probability of the state given the observation made in which case the numbers would have to add to one but it is the other way around A positive finding is equivalent to a likelihood finding consisting of all Os except a single 1 A negative finding is equivalent to a likelihood finding consisting of all 1s or some other nonzero number except a single 0 Two independent findings for a node can be combined by component wise multiplication of their likelihood vectors If they are not independent and it is too inaccurate to approximate them as JAVA VERSION 4 18 NETICA API 35 independent then they should be combined by adding 2 child nodes to the observed node in the original net one for each observation connecting them together to show the dependency and then entering positive findings for the child nodes Netica has functions for the direct entry of positive findings negative findings likelihood findings and also findings that a continuous node has a certain value If several findings are entered for the same node then it combines them as if they were independent observations and generates an error if they
82. e given name Returns a list of all the nodes in the net Returns a list of the parents of a node Returns a list of the children of a node Finds all the nodes that bear a given relationship such as D connected Markov blanket ancestors children etc with a given node Finds the nodes that bear a given relationship with a given set of nodes Change the order of a list of states to match a given node list To enter a case into a net and to read it out Saves a net s current set of findings to a file Reads findings from a file and enters into a net Retracts all findings i e the current case from a net Returns the joint probability of the findings entered so far The current case is used to revise each node s probabilities 108 Net Learner Net Caseset Caseset Caseset Caseset Caseset NetTester NodeList reviseCPTsByCaseFile learnCPTs generateRandomCase constructor finalize addCases addCases writeCases testWithCaseset mapStateList NETICA API JAVA VERSION 4 18 Reads a file of cases to revise probabilities Learn CPTs from case data with choice of algorithm Generates a random case in a net according to the net s distribution Creates a new case set object initially with no cases Deletes and frees all resources used by a case set object Searches the given database adding cases to a case set object Adds the cases located in the given case file Writes all the cases in the given case set to a file stream Performa
83. e library of built in functions which you can use in your equations The probability distribution functions all have a name that ends with Dist e g NormalDist Their first argument is always the node for which the distribution is for So if node X has parent m you could write JAVA VERSION 4 18 NETICA API 93 P X m NormalDist X m 0 2 to indicate that X has a normal Gaussian distribution with mean given by parent m and a standard deviation of 0 2 Common Math abs x absolute value sqrt x square root positive exp x exponential e x log x logarithm base e log2 x logarithm base 2 log10 x logarithm base 10 sin x sine x is in radians cos x cosine tan x tangent asin x arc sine result is in radians acos x arc cosine atan x arc tangent atan2 y xX atan y x but considers quadrant sinh x hyperbolic sine cosh x hyperbolic cosine tanh x hyperbolic tangent floor x floor highest integer lt x ceil x ceiling lowest integer 2 x integer x integer part of number same sign frac x fraction part of number same sign NETICA API Special Math JAVA VERSION 4 18 round x roundto dx x approx eq x y eqnear reldiff x y clip min max x sign x xor bi bo by increasing Xj Xo Xn increasing eq Xj Xz es Xn min Xi X2 Xn max Xi Xo Xn argminO 1 Xo Xi Xn argmax0 1 X
84. each net i e how likely you think each net is before seeing any data One approach is to say that each net is equally likely in which case the term can simply be ignored since it will contribute the same amount for each candidate net Another is to penalize complex nets by saying they are less likely which is of more value when doing structure learning Netica bases the prior probability of each net on the experience and probability tables that exist in the net before learning starts which appears to be a unique and elegant approach If the net has not been given any such tables then Netica considers all candidate nets equally likely before seeing any data The first term log P D N is known as the net s log likelihood If the data D consists of the n independent cases dj do dn then the log likelihood is log P D N log P d N P d2 N P dalN log P d N log P d2 N log P d N Each of the log P di N terms is easy to calculate since the case is simply entered into the net as findings and Netica s regular inference is used to determine the probability of the findings Both EM and gradient descent learning work by an iterative process in which Netica starts with a candidate net reports its log likelihood then processes the entire case set with it to find a better net By the nature of each algorithm the log likelihood of the new net is always as good as or better than the previous That process is repe
85. ean which indicates whether the event occurs Each of the p are the probability that b will be required to cause e If inh is zero and only one possible requirement is FALSE say b then the probability for e is 1 p If more possible requirements are FALSE the probability will be lower And if inh is nonzero the probability will be lower Reducing a pi always results in the same or higher P e p can be considered the strength of the relation between e and b with zero indicating independence link could be removed and 1 indicating maximum effect See also NoisyOrDist NoisyMaxDist Lalli NoisySumDist For documentation contact Norsys to obtain the document titled Noisy Or Max Sum NoisyOrDist e leak bi pi Dn Pn Lalli P e 1 1 leak product i 1 to n b 1 p 1 Required 0 lt p lt 1 0 lt leak lt 1 e b boolean Use this distribution when there are several possible causes for an event any of which can cause the event by itself but only with a certain probability Also the event can occur spontaneously without any of the known causes being true with probability leak make this zero if it can t occur spontaneously Each b isa booleanvariable which may cause the event when its TRUE e is also a boolean which indicates whether the event occurs Each of the p are the probability that e will occur if b is TRUE in isolation If leak is zero and only one possible cause is
86. earning nodes If every case supplies a value with certainty for each of the variables then the learning process is greatly simplified If not there are varying degrees of partial information 1 If there is a variable for which none of the cases have any information that variable is known as a latent variable or hidden variable 2 Ifsome cases have values for a certain variable and others don t that is known as missing data 3 Some values for variables may not be given with certainty but only as soft findings It may seem strange to be learning a net that has latent variables since none of the training cases have any information on them You introduce a latent variable as a parent node or intermediate node of multiple child nodes and Netica uses the correlations among the children to determine relationships between the latent node with others The result may be a Bayes net that is actually simpler has fewer CPT entries and generalizes better i e performs better on new cases seen For an example of using Netica to learn a latent variable see the Learn Latent dne net in the examples folder of the Netica Application distribution or get it from the Norsys net library 6 1 Algorithms There are three main types of algorithms that Netica can use to learn CPTs counting expectation maximization EM and gradient descent Of the three counting is by far the fastest and simplest and should be used whenever it
87. eft hand side of equation 85 legal disclaimer 2 libNeticaJ jnilib 10 libNeticaJ so 10 libraries Bayes net 20 61 node 61 license agreement 9 License Agreement pdf file 9 10 license for other languages 9 license password 9 likelihood in case file 47 in UVF file 44 likelihood finding 34 See also soft finding not independent 35 likelihood vector 35 link adding 30 link name 62 in equation 89 links 21 Linux 7 Lisp 6 lists of nodes 77 log likelihood during learning 48 logarithmic distribution eqn function 99 logarithmic loss 57 logarithmic series distribution eqn function 99 LogarithmicDist eqn function 99 logfactorial eqn function 99 loggamma eqn function 99 lognormal distribution eqn function 99 LognormalDist eqn function 99 log Weibull distribution eqn function 98 NETICA API JAVA VERSION 4 18 M Macintosh 7 MakeDecision java example program 68 MakeDecision java file 10 markov blanket 79 markov_blanket passed to getRelatedNodes 79 Matlab 6 max eqn function 100 maximizing expected utility 67 maximum likelihood learning 48 medical domain 20 22 member eqn function 100 memory required 22 min eqn function 100 missing data 37 47 50 missing state reading case 37 modeling agents 60 modifying nets 60 most informative test 82 MS Access 40 MS SQL Server 40 MS Windows 7
88. eldName 10 4 Sensitivity Of significant importance in Bayes net work is a measure of the independence between various nodes of the net Using just the link structure and d separation rules you can determine which nodes are completely independent of which other ones see the Graph Algorithms section above and how that changes as findings arrive However dependence is a matter of degree and using Netica s sensitivity functions you can efficiently determine how much an as yet unknown finding at one node will likely change the beliefs at another node There are many varied uses for the sensitivity measure During diagnosis it can specify which nodes will be the most informative in crystallizing the beliefs of the most probable fault nodes As findings arrive it will adjust to account for the new findings always identifying where further information would be useful to complete the diagnosis in a most intelligent manner In a net built for classification you can determine which features are the most valuable for performing the classification i e feature selection In an information gathering environment you can identify which are the most important questions to ask at each point to provide information on the variables of interest based on the answers to questions already received so as to avoid asking unnecessary or irrelevant questions When building a model of the 82 NETICA API JAVA VERSION 4 18 world such as an e
89. en it may be considered as a knowledge base Sometimes nets that are built to be used only once are constructed automatically on the fly perhaps by pasting together pieces of nets from libraries using templates Then the libraries and templates together make up a knowledge base Netica is designed to work for either type of application It allows probabilities to be entered directly perhaps originally coming from an expert and it can learn probabilities from data It will not handle templates directly but it has the facilities for libraries and on the fly construction that such a program requires A classic example of the use of Bayes nets is in the medical domain Here each new patient typically corresponds to a new case and the problem is to diagnose the patient i e find beliefs for the undetectable disease variables or predict what is going to happen to the patient or find an optimal prescription given the values of observable variables symptoms A doctor may be the expert used to define the structure of the net and provide initial conditional probabilities based on his medical training and experience with previous cases Then the net probabilities may be fine tuned by using statistics from previous cases and from new cases as they arrive JAVA VERSION 4 18 NETICA API 21 When the Bayes net is constructed one node is used for each scalar variable which may be discrete continuous or propositional true false Because of this
90. enters into a net Writes all the cases to a file in CSV or UVF format Makes the case set object consist of the cases located in the file Reads a file of cases to revise probabilities Name of file with full path that net was last written to or read from 106 Findings Evidence Node finding enterState Node finding enterStateNot Node finding enterReal Node finding enterLikelihood Node finding enterGaussian Node finding enterInterval Node finding setState Node finding setReal Node finding getState Node finding getReal Node finding getLikelihood Node finding getKind Node finding clear Net retractFindings Net getFindingsProbability Compiling Net compile Net uncompile Net sizeCompiled Net reportJunctionTree Net g setElimOrder Net g setAutoUpdate Node equationToTable NETICA API JAVA VERSION 4 18 Enters a discrete finding that a node is in a given state Enters a discrete finding that a node is not in a given state Enters a real number finding for a continuous node Enters a likelihood finding for a node i e a soft finding Enters a finding given by a Gaussian normal distribution Enters a finding uniform over an interval zero outside Enters a discrete finding overriding any previous entry Enters a real number finding overriding any previous entry Returns the finding for a node if there is one Returns the real number finding entered for a continuous node Returns the acc
91. ere are some of the most basic functions using NodeLists NodeList Net getNodes Returns a list of all the nodes in the net NodeList Node getParents Returns a list of the parents of a node NodeList Node getChildren Returns a list of the children of a node void Node getRelatedNodes NodeList relatedNodes String relation Finds all the nodes that bear a given relationship such as D connected Markov blanket ancestors children etc with a given node void Net getRelatedNodes NodeList relatedNodes String relation NodeList nodeList Finds the nodes that bear a given relationship with a given set of nodes Static int NodeList mapStateList int srcStates NodeList srcNodes NodeList destNodes Returns an array of the same states as srcStates which is in same order as srcNodes but in the order of destNodes And here are all the Nodeset functions void Node addToNodeset String nodeset Adds this node to the node set of the given name void Node removeFromNodeset String nodeset Removes this node from the node set of the given name boolean Node isInNodeset String nodeset Returns whether this node is a member of the given node set String Net getAllNodesets boolean includeSystem Returns a list of all node sets defined for this net separated by commas in priority order The argument indicates whether to include Netica s built in nodes sets otherwise it only puts user defined ones JAVA VERSION 4 18 NETICA
92. ervation of nodeP or that the two nodes are statistically correlated Finally the conditional probability tables CPTs are added For each node these are the probabilities of each of its states conditioned on the states of its parent nodes They are built up by multiple calls to NodeEx setCPTable which is defined in NodeEx java as a convenient way to call Node setCPTable The first argument in each call is the names of the conditioning states of its parents as a String Finally comes a list of numbers being the probabilities for each of the states of the node For example cancer setCPTable smoker 0 1 0 9 means that the probability that cancer is in its first state given that its parent is in state smoker is 0 1 and the probability that it s in its second state is 0 9 In probabilistic notation P cancer present smoking smoker 0 1 As another example tbOrCa setCPTable present absent 1 0 0 0 means P TbOrCa true Tuberculosis present Cancer absent 1 0 If is used as the name of a conditioning state then it will apply to all values of that parent node Likewise State EVERY_STATE can be used with setCPTable There is one thing to be cautious of when using setCPTable If speed is critical and you must set large probability tables use Node setCPTable instead of NodeEx setCPTable For example tbOrCa setCPTable TbOrCa present absent 1 0 0 0 could be accomplished by parentStates 0
93. es Each case i e record represents an example event object or situation in the world presumably that exists or has occurred and the case supplies values for a set of variables which describes the event object etc as specified in the previous chapter Each variable will become a node in the learned net unless you want to ignore some of them and the possible values of that variable will become the node s states The learned net can be used to analyze a new case which comes from the same or appropriately similar world as the training cases did Typically the new case will provide values for only some of the variables These are entered as findings and then Netica does probabilistic inference to determine beliefs for the values of the rest of the variables for that case Sometimes we aren t interested in values for all the rest of the variables but only some of them and we call the nodes that correspond to these variables target nodes If the links of the net correspond to a causal structure and the target nodes are ancestors of the nodes with findings then you could say that the net has learned to do diagnosis If the target nodes are descendants then the net has learned to do prediction and if the target node corresponds to a class variable then the net has learned to do classification Of course the same net could do all three even at the same time The Bayes net learning task has traditionally been divided into two p
94. esultant beliefs for each of the nodes of the original Bayes net which it attaches to the nodes so that you can retrieve them You may then enter some more findings to be added to the first or remove some findings and when you request the resultant beliefs belief updating will be performed again to take the new findings into account The amount of memory required by the junction tree and the speed of belief updating are approximately proportional to each other and are determined by the quality of the compilation The quality of the compilation depends upon the elimination order used which is a list of all the nodes in the net Any order of the nodes will produce a successful compilation but some do a much better job than others You may specify an elimination order perhaps from your own program or by using Netica Application s optimize compile or just let Netica API find a good one itself 3 3 Example of Probabilistic Inference Now let s look at an example of using the Netica API to do probabilistic inference In this example we will read in a simple Bayes net from a file compile it into a form suitable for fast inference enter some findings and see how the beliefs of a particular node change with each finding The example program DoInference java can be found in the examples directory of the Netica J installation The net we will use called ChestClinic is shown below Although reasonable it is a toy medical diagnos
95. et to be used for anything practical would define the X ray outcome in more detail but this will do for the example We enter this finding into the net with xRay finding enterState abnormal Then we use Node getBelief to cause belief updating to occur again to incorporate the latest finding and return the probability that the patient has tuberculosis given that his X ray came out abnormal The probability has now jumped to 9 24 so we ask him if he has recently made a trip to Asia When he answers to the affirmative and we enter that finding we then get a tuberculosis probability of 33 8 Exercise for the Reader After further testing you might discover that our patient has lung cancer and want to enter that as a finding The lung cancer explains away the abnormal X ray and so our probability that he has tuberculosis would fall to 5 00 Try editing and running DolInference java The output produced will be gt java DoInference The probability of tuberculosis is 0 0104 Given an abnormal X ray the probability of tuberculosis is 0 0924109 Given an abnormal X ray and a visit to Asia the probability of tuberculosis is 0 337716 Given abnormal X ray Asia visit and lung cancer the probability of tuberculosis is 0 05 26 NETICA API JAVA VERSION 4 18 For examples involving more complex types of findings and the retraction of findings see the Findings and Cases chapter JAVA VERSIO
96. etica finds are the ones that provide the highest expected value of the utility node or the sum of the utility nodes if there are more than one The above program uses Node getStateFuncTableQ to access this decision function and prints out the following If the forecast is sunny the expected utility of take umbrella is 24 205606 of dont_take_ umbrella is 91 58878 If the forecast is cloudy the expected utility of take umbrella is 37 44186 of dont_take_ umbrella is 65 11628 If the forecast is sunny the best decision is dont take umbrella If the forecast is cloudy the best decision is dont_take_ umbrella If the forecast is rainy the best decision is take umbrella JAVA VERSION 4 18 NETICA API 71 Note that Node getExpectedUtilsQ or Node getBeliefs must be called before Node getStateFuncTable to have Netica build the decision table and again after entering findings if you want it optimized for the new findings For more information on decision nets in general and using Netica to work with them see the onscreen help system of Netica Application and there is also some information in the tutorial at the Norsys website 72 NETICA API JAVA VERSION 4 18 9 Drawing Nodes and Nets Netica J includes several Java SWING components for displaying Netica nets and nodes The color layout and general appearance of the displayed components are very similar to the style used in the Netica Application program see http www
97. etwork fragments and then stitch them together on the fly to create models Finally it discusses transforms that may be done on a Bayes net to remove nodes or reverse the direction of links while maintaining the overall probabilistic relationship between the remaining nodes 7 1 Common Modifications Most of the functions introduced previously for building a Bayes net can also be used to modify it For instance new Node and Node addLink can introduce new variables or dependencies and Node delete and Node deleteLink can remove them Almost every property of nets and nodes can be altered Even decision nodes can be converted to nature nodes Node setKind or vice versa without losing their CPT tables or other properties That can be useful to model situations with multiple agents where the nodes that are the decisions of one agent are nature nodes to the other agents First the optimal decisions are found for the first agent and then those decision nodes are converted to nature nodes when finding the optimal decisions for the next agent When adapting a net to a new environment states can be added Node addStates removed Node state delete or the order of the states may be changed Node reorderStates In each case the tables of the nodes being changed and the tables of their children will be appropriately modified JAVA VERSION 4 18 NETICA API 61 The node tables themselves may be modified Perhaps CPTs need
98. evidence See also findings functions available 106 example Bayes nets 27 example DNET file 31 example program building decision net 68 displaying a Bayes net graphically 72 Dolnference java 23 DrawNet java 72 entering findings 35 LearnCPTs java 52 learning probabilities 52 MakeDecision java 68 NetTester java 57 node library 62 probabilistic inference 22 SimulateCases java 38 solving decision problem 68 examples directory 11 exception handling 18 exclude_self passed to getRelatedNodes 79 executeSQL DatabaseManager 41 exhaustive 29 experience 50 explaining away 25 exponential distribution eqn function 97 ExponentialDist eqn function 97 extreme value distribution eqn function 98 ExtremeValueDist eqn function 98 F factorial eqn function 98 fadeCPTable Node 55 fading 55 FDist eqn function 98 F distribution eqn function 98 feature list 7 file format case file 37 DNE Bayes net 14 file operations functions available 105 files provided in distro 10 finalize 19 finalize Caseset 40 finalize Environ in use 23 finalize Net in use 23 38 68 finalize Sensitivity 82 finalizers 19 finding 21 consistency 35 entering 35 JAVA VERSION 4 18 likelihood 34 negative 34 positive 34 sets of 36 soft 34 findings node 64 FIRST_CASE in use 52 Fisher Snedecor distribution eqn function
99. f a node called Weather connected to a node called Forecast The link between them could go either way since we can t really capture causation they are both caused by other variables like the previous weather but say you put the link from weather to forecast because often it s better to put links from more immutable to less immutable variables Each day you revised its probabilities so that eventually it accurately captured the probabilistic relationship between the morning weather forecast and the weather for that day Then you could put it in a library to later graft into nets for inference involving the weather and its forecast such as the decision problem discussed in the Decision Nets chapter 1 flow_rate x3 instrument_status temperature instrument As another example suppose you have a device for measuring the flow rate in a pipe This sensor will produce biased readings depending on the ambient temperature and it can break in a few different ways each of them producing wrong or inaccurate readings You can model the sensor with a 4 node net 1 node for the reading on the sensor and 3 parent nodes corresponding to actual flow rate ambient 62 NETICA API JAVA VERSION 4 18 temperature and sensor status okay broken_1 broken_2 etc You enter the probabilistic relationship and then you disconnect the node from its parents and place it in a library so it appears as in the above diagram disconnection and graft
100. f you need to build a more sophisticated graphical application for selecting nodes entering findings and such you may wish to use this program as a starting point 76 NETICA API JAVA VERSION 4 18 9 7 Miscellaneous Useful Features The NetPanel class supports the concept of a selection set which is just a NodeList of nodes in the hilited state see NodePanel getDisplayMode Also you may choose to display a subset of the nodes in a net using the setSubnet method 9 8 Feedback Wanted We would appreciate hearing whether you find the gui package useful and how you might like to see it evolve JAVA VERSION 4 18 NETICA API 77 10 Special Topics 10 1 Node Lists and Node sets Many operations in intelligent computing require working with lists of variables and when using Bayes nets that means working with lists of nodes so it is not surprising that many Netica functions take node lists as arguments At first it might not be clear why Netica has two classes to work with sets of nodes but their purposes are very different Netica s workhorse node list class is NodeList whose main purpose is to pass an ordered list of nodes to Netica J or retrieve such a list from Netica J It extends java util Vector but requires that all of its elements be Nodes and that they all come from the same Net The other class is Nodeset which is just meant to access node sets defined in Netica Application Netica Application has a convenient
101. g If you had to supply a probability that you were going to draw a white ball it would be 0 5 providing you had no additional information Contrast this with the case where you can count the balls in the bag beforehand there are 10 of each and you will shake the bag before you draw In this situation the probability of drawing a white ball is 0 5 but whereas in the first case you were in a state of ignorance now you feel much more informed If you needed to do probabilistic inference or solve decision problems as in the previous chapters then the 0 5 probability would be sufficient in either situation In both situations you should believe and act as if there was an equal chance of drawing a white or a black ball So the concept of experience is not required for these types of problems and you do not have to be able to represent ignorance ignorance is the endpoint of the experience spectrum However for learning and communicating knowledge it is useful to be able to represent the degree of experience as well as the probability as we shall see If you are going to sequentially draw a number of balls from the bag then things are different If you drew 4 white balls in a row then in the first situation your probability that the next ball will be white should be greater than 0 5 because you are learning perhaps incorrectly that there seem to be a lot of 50 NETICA API JAVA VERSION 4 18 white balls In the second situation your p
102. getInputIndex temperature rtemp instrument1 switchParent instrument1 getInputIndex instrument_status status instrument2 switchParent instrument2 getInputIndex flow_rate flow2 instrument2 switchParent instrument2 getInputIndex temperature rtemp instrument2 switchParent instrument2 getInputIndex instrument_status status Now the application net appnet is ready for probabilistic inference Perhaps we have positive findings for the instrument node i e what we read from its dial and we use them to determine flows and their uncertainties in a way that properly accounts for random uncorrelated and systematic correlated errors as well as all the background knowledge about the situation 7 2 Net Reduction Suppose you have a large net that has been constructed over time by a combination of expert assistance and probability learning It shows the relationships between hundreds of variables and contains much valuable information that could be used in a number of different applications Now you want to use it in an application where only 10 of the variables are of interest to you In every query of the new application four of them will always have the same value For instance one of the nodes in the original net might by Gender and in the restricted application the net will only be used for females so we would like to enter a permanent finding of female for the node Gender These nodes are called conte
103. ght be an adaptive Bayes net which is constantly receiving new cases and doing inferences while it slowly changes to match a changing world Netica achieves this partial forgetting of the past by using fading Every so often you call Node fadeCPTable passing it a degree between 0 and 1 and it will reduce the experience and smooth the probabilities of the node by an amount dictated by the degree A degree of 0 has no effect while a degree of 1 does complete forgetting resulting in uniform distributions with no experience Calling fadeCPTable once with degree 1 a and again with degree 1 b is equivalent to a single call with degree 1 ab During fading each of the probabilities in the node s conditional probability table is modified as follows where prob and exper are the old values of probability and experience and prob and exper are the new values prob normalize prob exper 1 degree degree BaseExper where BaseExper is normally 1 see section 7 1 exper is obtained as the normalization factor from above remember that there is one experience number per vector of probabilities So prob exper prob exper 1 degree degree BaseExper When learning in a changing environment you would normally call fadeCPTable every once in a while so that what has been recently learned is more strongly weighted than what was learned long ago If an occurrence time for each case is known and
104. gs that have been entered for node thereby undoing all of the above and step 11 enters the positive finding that the value of node is state 2 which won t generate an error this time like it would have in step 7 When getState is called in step 12 it will now return 2 and the values of clike after step 13 will be clike 0 0 0 clike 1 0 0 clike 2 1 0 clike 3 0 0 5 1 Cases and Case Files The set of all findings entered into the nodes of a single Bayes net is referred to as a case A case may be saved to a file for later retrieval Case files may consist of a single case or of many cases Case files act as databases they may be used to swap cases in and out of a net as additional findings are obtained or beliefs required to transfer a case from one net to another or as data to learn a new net Some ways you can make a case file are e Use a text editor to manually construct it according to the specification below e Write a program whose output is a case file e Export it as a CSV or tab delimited text file from a spreadsheet or database program Or you can copy from the spreadsheet or database program paste into a text editor and save as a text file JAVA VERSION 4 18 NETICA API 37 Extract it from a database using Caseset addCases DatabaseManager followed by Caseset writeCases e Use Netica Application to enter findings by pointing and clicking and then choose Save Case from the menu e Call
105. having probability p i 1 m and we are interested in the number of occurrences of each outcome ki given that a total of n trials are performed To create a multinomial distribution between the k and n nodes first add to the net a new boolean node in this example called be Then add links from the nodes of all the non fixed parameters usually n and all k to node be At node be put an equation with MultinomialDist and convert the equation to a table Finally give node be a finding of true Normally the sum of p is one but Netica will just normalize the p if that is not the case If m is 2 then ky is deterministically determined by k i e ky n k and k is distributed by BinomialDist Each of the k separately has a binomial distribution with parameters n and pi and because of the constraint that the sum of the k s is n they are negatively correlated The Dirichlet distribution is the conjugate prior of the multinomial in Bayesian statistics For assistance on using this function contact Norsys support norsys com nearestO val Xo X1 Xn is t nearestl val x1 X2 Xn val x lt val x xi x for all j where val and x are unrestricted real numbers JAVA VERSION 4 18 NETICA API 101 Returns the index position in list of the argument with the value closest to val as measured by the absolute value of the difference If there are several with the same smallest difference the
106. he findings currently entered The measures can be in the form of mutual information entropy reduction or the expected reduction of real variance e Advanced Decision Nets Can solve influence diagrams which have multiple utility and decision nodes to find optimal decisions and conditional plans using a junction tree algorithm for speed Handles multi stage decision problems where later decisions depend on the outcomes of earlier ones and on observations not initially known No forgetting links need not be explicitly specified e Junction Tree Algorithm Can compile Bayes nets and influence diagrams into a junction tree of cliques for fast probabilistic inference An elimination order can be specified or Netica can determine one automatically and Netica can report on the resulting junction tree e Soft Evidence Accepts likelihood findings i e virtual evidence findings of the form that some variable is not is some state Gaussian findings and interval findings as well as regular real valued or state findings e Link Reversal Can reverse specified links or sum out absorb nodes of a Bayes net or influence diagram while maintaining the same overall joint probability distribution properly accounting for any findings in the removed nodes or other nodes e Disconnected Links Links may be individually named and disconnected from parent or child nodes thus making possible libraries of network fragments which you may then copy an
107. hitis net getNode Bronchitis The observed nodes are typically the factors known during diagnosis NodeList testNodes new NodeList net testNodes add cancer The unobserved nodes are typically the factors not known during diagnosis NodeList unobsvNodes new NodeList net unobsvNodes add bronchitis unobsvNodes add tuberculosis 58 NETICA API JAVA VERSION 4 18 unobsvNodes add tbOrCa net retractFindings IMPORTANT Otherwise any findings will be part of tests net compile NetTester tester new NetTester testNodes unobsvNodes 1 Streamer inStream new Streamer Data Files ChestClinic cas Caseset testCases new Caseset testCases addCases inStream 1 0 null tester testWithCaseset testCases printConfusionMatrix tester cancer System out printin Error rate for cancer getName tester getErrorRate cancer System out printin Logarithmic loss for cancer getName tester getLogLoss cancer the following are not strictly necessary but a good habit testCases finalize tester finalize net finalize catch Exception e e printStackTrace y Print a confusion matrix table public static void printConfusionMatrix NetTester nt Node node throws NeticaException int numStates node getNumStates System out printin nConfusion matrix for node getName for int i 0 i lt numStates
108. ibution logfactorial n log n n 1 n 2 1 where n20 nis an integer Returns the natural logarithm of the factorial of n that is log n You could also use the factorial function but this helps to avoid overflow when n is large gt 170 If n is not an integer you may want to use the Loggamma_ function which for integer values is related to Llogfactorial by logfactorial n loggamma n 1 but whichis also defined for non integer values loggamma x log gamma x where x20 Returns the natural logarithm of the gamma function of x It may be used to avoid overflow when x is large The gamma function is normally defined for negative values of x as well but Netica cannot compute these LognormalDist x amp 6 La N log x amp x where N is the normal distribution 1 x sqrt 2n exp Cog x o 2 Required gt 0 The lognormal distribution results when the logarithm of the random variable is described by a normal distribution NormalDist This is often the case for a variable which is the product of a number of random variables by the central limit theorem Notice that the n of Lognormal is not capitalized indicating that this is not the same as the logarithm of the normal distribution 100 NETICA API JAVA VERSION 4 18 max xX1 X2 Xn x s t xi gt xj for all j where x are unrestricted real numbers Returns the maximum of x1 X2 Xn At le
109. ica API call for reading the NETA file is the same as for a DNET file Netica will recognize each and handle it appropriately If you wish you can encrypt the net so that only software that knows the password will be able to read it JAVA VERSION 4 18 NETICA API 33 Streamer stream new Streamer Built_ChestClinic neta stream setPassword MyPassword123 net write stream writes an encrypted file Encryption is useful when you need to distribute the net with your application for Netica API to use but the net contains proprietary information Encrypted nets can also be read or created by Netica Application provided that the user enters the correct password For a full code example including reading encrypted files see the javadocs for Streamer setPassword There are a number of other functions that may be used when constructing a net For a list of them see the Low Level Net Modification section of the Functions by Category chapter and for detailed descriptions of each one see the javadocs for the Net class For another example of constructing a net which demonstrates how to build a decision net create decision and utility nodes and work with 3 state and continuous nodes see the Decision Nets chapter 34 NETICA API JAVA VERSION 4 18 5 Findings and Cases In the Probabilistic Inference chapter we saw how to enter positive findings into a Bayes net to do probabilistic inference findings are also
110. in J Royal Statistics Society B 50 2 157 194 Cowell Robert G Dawid A P et al 1999 Probabilistic Networks and Expert Systems Springer Verlag Spiegelhalter David J Philip Dawid et all 1993 Bayesian analysis in expert systems in Statistical Science 8 3 219 283 Neapolitan Richard E 2004 Learning Bayesian Networks Pearson Education Inc Prentice Hall Korb Kevin and Ann E Nicholson 2004 Bayesian Artificial Intelligence Chapman amp Hall CRC Shachter Ross D 1986 Evaluating influence diagrams in Operations Research 34 6 871 882 Shachter Ross D 1988 DAVID Influence diagram processing system for the Macintosh in Uncertainty in Artificial Intelligence 2 John F Lemmer and L N Kanal Eds North Holland Amsterdam Shachter Ross D 1989 Evidence absorption and propagation through evidence reversals in Uncertainty in Artificial Intelligence 1989 303 308 JAVA VERSION 4 18 NETICA API 105 13 Functions by Category System Environ constructor Environ finalize Environ g setArgumentChecking Environ getVersion getVersionString Environ g setMemoryUsageLimit Environ g setCaseFileDelimChar Environ g setMissingDataChar Error Handling NeticaError getMessage NeticaError isInCategory NeticaError getSeverity NeticaError getIdNumber Environ g setArgumentChecking File Operations Streamer Streamer Streamer Streamer Environ Environ Caseset
111. individuals frequencies of words size of particles size of towns cities areas burnt in forest fires size of some fractal features etc These are situations where there are many that are small and a few that are large like the Pareto principle in which 20 of the population owns 80 of the wealth For any value of a the distribution is scale free which means that no matter what range of x one looks at the proportion of small to large events is the same 1 e the slope of the curve on any section of the log log plot is the same k PoissonDist k p Wallin E e Required k gt 0 u gt 0 k is an integer If events occur by a Poisson process then the number of events that occur in a fixed time interval is described by the Poisson distribution where p is the average number of events per unit time round x floor x 1 2 where x is an unrestricted real Rounds x to the nearest integer To round off to other quantities use roundto roundto dx x dx floor x dx 2 dx where dx gt 0 Rounds x to the nearest dx which may be less than or greater than 1 For example roundto 10 17 rounds 17 to the nearest 10 and so it returns 20 Ifdx 1 then this is the same as the round function selectO index Xo X1 Xn x s t i index select1 index x1 X2 Xn where index is integer x are all the same type select0 0 S index lt n selectl 1 index n Returns the value of the x argument at positi
112. ing Bayes nets 20 BuildNet java file 10 built in constants for equations 92 built in functions for equations 92 built in operators for equations 92 JAVA VERSION 4 18 C C 6 calcState 84 calcValue 84 case 36 identification number 37 case file 36 comments 37 creating 36 example 38 format 37 uncertain findings in 42 CASE 1 in case file 37 cases functions available 107 case set 40 Caseset class 40 107 Caseset constructor 40 in use 41 57 Cauchy distribution eqn function 97 CauchyDist eqn function 97 causal network 20 chance node 67 ChestClinic example net diagram 23 DNET file 31 ChestClinic cas file 10 ChestClinic dne file 10 ChestClinic_WithVisuals dne file 10 chi square distribution eqn function 97 child nodes 21 children found by getRelatedNodes 79 ChiSquareDist eqn function 97 classification 7 46 ClassifyData java file 10 clear Node Value in use 35 clip eqn function 97 clique tree 22 Cobol 6 combining nets 60 comments 29 compile Net 24 in use 23 38 compile bat file 10 compiling functions available 106 compiling vs node absorption 65 complete uncertainty in UVF file 45 conditionals in equation 87 confidence 49 confusion matrix 57 conjugate gradient descent 49 connected nodes found by getRelatedNodes 79 connecting with a database 40 consistent findings 35 const
113. ing are explained below Later if you have a net to model a situation in which you have made two measurements with the device you just duplicate the device characteristics node from the library twice into the new net and graft it to the appropriate nodes in that net see diagram below Note that if the ambient temperature could be different between the two measurements then the room_temp node would appear as two connected nodes similar to the flow nodes and the same goes for the instrument_status node if the device may have broken between measurements Automating the process of net construction for new situations is an area of active research with dynamic Bayes nets templates and graph grammars being some of the methods used ow instrument_status instrument instrument2 Netica makes it easy to maintain libraries of disconnected nodes and subnets To make a new library just use new Net Nodes and subnets can be copied to it using Net copyNodes which can transfer material from one net to another and also copies all the links between nodes in a subnet When a node is being duplicated but one of its parents isn t then Net copyNodes will give the duplicated node a disconnected link where that parent was This is a link which only has a place holder for a parent and is meant to be reconnected to another node before being used for inference In this way the conditional probability relationship that the node had with its paren
114. ique within the object they apply to Comparisons are case sensitive In general Netica restricts names for all objects in this way If you find that overly restrictive then you can also give the object a title which is an unrestricted Unicode string Some objects can have a comment as well which is also an unrestricted Unicode string and it would not be out of the ordinary if this were thousands of characters long The states do not need to be named so instead of the list of state names a 2 could be passed to Node indicating the number of states the node can take on 0 would be passed for a continuous node Later the program could set the state names of the nodes using Node setStateNames Or they could be left unnamed but in general it is recommended to name them in order to keep track of the meanings of the states and to be able to refer to the states by names as was done in the last chapter Then a couple of 30 NETICA API JAVA VERSION 4 18 nodes are given titles which also aren t really required but are a bit more descriptive than their names the idea is to keep names short for convenience Next the nodes are linked together with Node addLink A call of the form nodeC addLink nodeP makes nodeP a parent of nodeC which means we wish to express the probabilities of nodeC as a function of i e conditioned on values of nodeP Usually the link indicates that nodeP causes nodeC that nodeC is an imperfect obs
115. is example from LauritzenSpiegelhalter88 that has often been used in the past for demonstration purposes To a certain degree the links of the net correspond to causation The two top nodes are predispositions which influence the likelihood of the diseases in the row below them At the bottom are JAVA VERSION 4 18 NETICA API 23 symptoms for the disease Each possible state of the node is shown in the box Ignore the bars for now they were produced by the Netica Application program and just show the probabilities of each state before any findings have arrived Visit To Asia Smoking _ visit 1 00 smoker 50 0 no visit 99 0 non smoker 50 0 Bronchitis present 1 04 present 5 50 present 45 0 absent 99 0 absent 94 5 absent 55 0 Tuberculosis or Cancer true 648 5 false 93 5 present 43 6 absent 564 Before the example program below will work the file containing the net ChestClinic dne must exist in the Data Files subdirectory of the directory running the program If you are running this example straight from examples directory of the Netica API distribution that will already be the case Otherwise you should obtain the file from the examples Data Files directory of the Netica API distribution Or you can build it yourself the next chapter shows how and at the end of that chapter is a file listing of the net it is missing the Bronchitis and Dyspnea nodes but they are not needed now anyway
116. isons into summary statistics If you want you can call testwithCaseset several times with different files to generate statistics for the combined data set JAVA VERSION 4 18 NETICA API 57 Finally you call functions to retrieve the actual performance statistics you desire You can obtain the error rate with NetTester getErrorRate the logarithmic loss with NetTester getLogLoss the quadratic loss with NetTester getQuadraticLoss and the whole confusion matrix with NetTester getConfusion Be sure to see the function documentation for each of these functions and NetTester and NetTester testWithCaseset for more details on the whole process Also you can contact Norsys for a document with more information on what the various measures mean Here is some example program that rates the toy Bayes net ChestClinic to test the Cancer node diagnosis assuming that the other disease nodes Tuberculosis Bronchitis TbOrCa are also unobserved nodes i TestNet java Example use of Netica J for testing the performance of a learned net with the net tester tool a import java io File import norsys netica public class TestNet public static void main String args try Environ env new Environ null Net net new Net new Streamer Data Files ChestClinic dne Node tuberculosis net getNode Tuberculosis Node cancer net getNode Cancer Node tbOrCa net getNode TbOrCa Node bronc
117. ist description The causes and even the link parameters can be more complex expressions For example p Bond NoisyOrDist Temperature BackTemp Bond 0 001 Pressure Switch Eff Temperature gt BackTemp Us 0 9 Pressure Switch high Eff 0 3 For more information on using Netica s Noisy Or Noisy And Noisy Max and Noisy Sum functions contact Norsys for the Noisy Or Max Sum document 92 NETICA API JAVA VERSION 4 18 11 11 Equation Constants Operators and Functions A Built in Constants The following constants may be used in equations pi 3 141592654 deg radian per degree pi 180 If you wish to have the constant e 2 7182818 in your equation use exp 1 B Built in Operators Both the functional and the operator notations shown below are accepted Functional Notation Operator Notation neg x not b IOD equal x y x y not equal x y x l y approx_eq x y x y less x y x lt y greater x y xX gt y less eq x y x lt y greater eq x y x gt y plus Xir Xo see Xn XK X minus x y x y mult Xi Xo Xn X X gt div x y x y mod x base x base power x y gt Oy and bi bo Gens by by amp amp bo amp amp or bi bo oe by b b2 if test tval fval test tval amp amp by bp fval C Built in Functions Netica contains an extensiv
118. it generates a random case from the ChestClinic net These cases will be distributed according to the probability distribution of that net Each case is saved to the case file named ChestClinic cas a sample of which we saw above We will use this case file in the next chapter Learning From Case Data Here is another example of a case file this time for cars brought into a garage notice BatAge which is a continuous variable gt CASE 1 gt Starts BatAge Cranks Lights StMotor SpPlug MFuse Alter BatVolt Dist PlugVolt false Deg false off fouled okay dead 2 false ES false off okay okay dead 2 none false Dia2 false off okay okay okay okay dead okay none true 4 1 true bright okay okay strong okay strong true 254 bright wide okay strong okay 2 true bright fouled okay okay strong false 1 true off okay okay okay okay dead 2 none true 2 9 true bright strong okay strong Timing good bad good good good 40 NETICA API JAVA VERSION 4 18 5 2 Casesets Netica J has a very powerful class called Caseset A Caseset instance represents a set of cases that may be in a database in memory or in a disk file in any of a number of formats You use the same functions to operate on Casesets no matter where they are or in what format they are To make a Caseset you first create an empty one with one of the Caseset constructors For example Caseset cs new Caseset Then
119. ithn 1 HypergeometricDist k n s N alll binomial s k binomial N s n k binomial N n Required N 2 0 Oo lt n lt Nn Oo lt s lt N k N n and s are integers This provides the probability that there are k successes in a random sample of size n selected without replacement from N items of which s are labeled success and N s labeled failure It is used in place of the binomial distribution BinomialDist for situations which sample without replacement increasing x1 X2 Xn X1 lt X2 amp amp X2 lt X3 amp amp KK Xn 1 lt Xn where x are unrestricted real numbers Returns TRUE iff each x is greater than the previous one If you wish the test to be greater than or equals use increasing eq increasing eq x1 X2 Xn X1 lt X2 amp amp X2 lt X3 amp amp amp amp Xn 1 lt Xn where x are unrestricted real numbers Returns TRUE iff each x is greater than the previous one If you wish the test to be just greater than use increasing LaplaceDist x u La 1 2B exp x n B Required B gt 0 Its pdf is two exponential distributions spliced together back to back The difference between two iid exponential distribution random variables follows a Laplace distribution Also known as the double exponential distribution LogarithmicDist k p ulh p k k log 1 p Required 0 lt p lt 1 k is an integer Also known as the logarithmic series distr
120. known as evidence A positive finding is the observation or knowledge that some discrete node definitely has a particular value However we may discover that some node definitely does not have some particular value and not have any more information to help us determine what value it does have This is called a negative finding For example say the node Temperature can take on the values cold medium and hot We may obtain information that the temperature is not hot although it doesn t distinguish between medium and cold at all This is a single negative finding If later we receive another negative finding that the temperature is not medium then we can conclude that it is cold So several negative findings can be equivalent to one positive finding A third type of finding is a soft finding also known as virtual evidence or likelihood finding In this case we receive uncertain information about the value of some discrete node It could be from an imperfect sensor or from a friend who is not always right Say we have a thermosensor to measure Temperature which is designed so that when the temperature is hot it is supposed to turn on In actual practice we find that when the temperature is cold the sensor never goes on when the temperature is medium it goes on 10 of time and when it is hot it always goes on If at a certain time we observe the sensor on and want to enter this finding into the Temperature node then w
121. license password to the Environ constructor For example Environ env new Environ your unique license If you do not have a license password then you can simply supply null in place of it in which case Netica J API will be fully functional but limited in problem size e g size of nets size of data sets The license password you have purchased also licenses you to use versions of Netica API for other languages such as the C version Netica C the C or Visual Basic version or the C version Simply supply that license string to the appropriate Environment constructor in those languages The same rights and obligations granted by the API license apply to all the language versions If your license password enables Netica API it will have a 310 within it The digit immediately following that is the version number of the license It must be at least 3 to fully enable this version 3 xx of Netica API If it is less then after you call new Environ a warning message will be available for viewing if you call NeticaError getWarnings and Netica API will continue operation in limited mode To upgrade your license contact Norsys or see https www norsys com order_v3_upgrade htm 10 1 3 Files Included NETICA API JAVA VERSION 4 18 The following files are included in the distribution of Netica J the Java version of Netica API Directory docs bin src neticaEx src neticaEx aliases
122. ll accumulate until the next getWarnings invocation whereupon they are cleared from the warnings list JAVA VERSION 4 18 NETICA API 19 2 7 Finalizers amp Memory Management For large networks and large node tables Netica can consume large amounts of memory Often Java developers cease to worry about memory management as the JVM s garbage collector will automatically collect Java objects that can no longer be referenced However the Java specification does not require that a JVM actually call the garbage collector whenever a Java object reference is no long used It may or may not do so and it may choose to do so on its own schedule Accordingly you may want to actively call the delete or finalize methods on resource hungry objects when you are done with those objects rather than wait for the JVM to free them For most Netica objects calling finalize frees all their native resources but not for Node and State objects For them finalize just indicates that you are done with the reference but the native resources won t be freed until the owning Net or Node is freed However calling Node delete will remove the Node from its owning Net and free its resources and calling State delete will remove the State from its owning Node and free its resources Note if you ever override the finalize method of any Netica J class be certain that you always call the base class finalizer method super finalize as your last in
123. lso known as normal soft finding where the m is the mean and s is the standard deviation Note that there cannot be any space before or after the The uncertainties in measurements from lab instruments or polling results are often expressed with a notation and indicate a Gaussian distribution so they can be easily input into Netica although in some contexts they may indicate an interval distribution which is described below Interval Syntax a b a and b are real numbers state names or state indexes preceded by Examples 0 10 3 2 27 lo med 1 3 This finding indicates the value is known to be within the two endpoints There may be spaces before or after the comma or brackets Intervals of states include both endpoints so lo med includes states lo med and any states between Intervals of continuous variables include the lower endpoint but not the upper endpoint so 0 10 for variable X means 0 lt X lt 10 Likelihood within the interval is one outside the interval it is zero Unbounded Interval Syntax gt b or lt b b is areal number state name or state index preceded by Examples gt 4 75 lt 10 lt med gt 2 This finding indicates that the value is above a certain point or below a certain point When b is a state the interval includes the endpoint when it is for a continuous variable the interval includes the endpoint only for gt intervals so gt is really gt The interval can p
124. m can be found in the examples directory of your Netica J distribution The program operates by first reading from file a very simple example net the net that was constructed in the Building and Saving Nets chapter and then duplicates it by making a new net and duplicating all the nodes into it Next it removes the probabilities and experience from the duplicated nodes with Node deleteTables The idea is to relearn approximations of those probabilities by using the case file ChestClinic cas that we created in the last chapter Findings and Cases In effect we start with a net that has the structure of ChestClinic dne but no probabilities and experience since they were deleted and then using a set of cases that match the probability distribution of that net we will learn a net that should have a similar probability distribution Of course the more samples that are in the case file the better the approximation to the original net The program reads all the cases with a single instruction reviseCPTsByCaseFile casefile learned_nodes 1 0 If instead we wanted to examine each case say to exclude outliers perform calculations on them or otherwise modify them we could have looped through the case file entering each as a finding and used the instruction reviseCPTsByFindings learned_nodes 1 0 to incrementally adjust the CPTs The comment section at the bottom of LearnCPTs java shows you how to use this alterna
125. n the index of the first occurrence will be returned The first x argument has index 0 if nearest0O is used or index 1 if nearest1 is used Must be passed at least 2 arguments val and an x See also member Example nearestO 1 1 3 4 1 3 4 returns 0 nearestl 563 6 6 3 4 126 returns 3 z KA 4 n k NegBinomialDist k n p binomial n k 1 k p 1 p Required 0 lt n 0 lt p lt 1 kandn are integers The negative binomial distribution is the distribution of the number of failures that occur in a sequence of trials before n successes have occurred in a Bernoulli process independent trials with outcomes labeled success or failure and constant probability p of success The limit of a negative binomial distribution as n 1 p 0 n 1 p A isa Poisson distribution with parameter If n 1 then this distribution is just the geometric distribution NoisyAndDist e inh bi pi bp Pn Wla P e 1 inh product i 1 to n b 1 1 p Required 0 lt p lt 1 O0 lt inh lt 1 e b boolean Use this distribution when there are several possible requirements for an event and each has a probability that it will actually be necessary Each of the necessary requirements must pass for the event to occur Even then there is a probability given by inh that the event may not occur make inh zero to eliminate this Each b is a booleanvariable which when TRUE indicates a requirement passed e is also a bool
126. nce tests a Bayes net with a set of cases Change the order of a list of states to match a given node list Sensitivity to Findings Utility Free Value of Information Sensitivity Sensitivity Sensitivity Sensitivity Performance Testing a Net NetTester NetTester NetTester NetTester NetTester NetTester NetTester constructor finalize getVarianceOfReal getMutualInfo constructor finalize testWithCaseset getConfusion getErrorRate getLogLoss getQuadraticLoss Database Connectivity DatabaseManager DatabaseManager DatabaseManager Caseset DatabaseManager DatabaseManager High Level Net Modification constructor finalize insertFindings addCases executeSql addNodes See also Learning from Data Node Net Node Node reverseLink absorbNodes equationToTable switchParent duplicateNodes copy constructor undoLastOperation redoOperation Creates an object to measure sensitivity Deletes the sensitivity measuring object Measure the expected reduction in variance due to a finding Measure the mutual information entropy reduction Creates a new tester object for given tests on given nodes Deletes a tester object Reads the cases one by one and for each it does inference and grades the Netica net gathering statistics Returns a confusion matrix result of the testing Returns the error rate result of the testing Returns the logarithmic loss result of the testing Returns the quadra
127. not a deadlock concern since the executing Netica J function will not be waiting on any other thread unless you do that yourself through the use of Netica J callbacks 2 4 Event Handling If you wish your program to receive events Netica J has the ability to call your program when certain types of events occur Any Java object can choose to listen to Netica events by simply implementing the NeticaEventListener interface and asking the node or net that generates the events to add itself to that node or net s listener list The methods Node addListener and Net addListener are supplied for this purpose Since Node and Net objects are already NeticaEventListeners they each possess an eventOccurred NeticaEvent method If you should choose to override this method it is important that you call the base class method super eventOccurred event in your method so that this node or net will still be able to handle deleting events properly Currently events are generated for the creation removal and duplication of Nodes and Nets Future versions of Netica J will include more types of events If you have a request please let us know 2 5 Java Objects and Native Object Peers Since Netica J is a JNI API many of the Java objects created are proxies of their native or peer counterpart objects internal to the core Netica binary This is true of Environ Net Node NetTester NeticaError Sensitivity and Streamer The remaining
128. ntered so far Finds the state for each node which results in the most probable explanation MPE Creates a case sampled from the net given the current findings Removes the given nodes while maintaining the joint distribution of the remaining nodes Measures the mutual information between two nodes Measures how much a finding at one node is expected to reduce the variance of another node Returns the state of a node calculated from its neighbors if that can be done deterministically Returns the numeric value of a node calculated from its neighbors if that can be done deterministically JAVA VERSION 4 18 Learning From Data Net Net Learner Learner Learner Learner Learner Node Node Node Node Node reviseCPTsByCaseFile reviseCPTsByFindings constructor finalize learnCPTs g setMaxIterations g setMaxTolerance fadeCPTable getCPTable getExperTable setCPTable setExperTable Decision Nets Node getExpectedUtils Node setKind Node Lists NodeList constructor NodeList add NodeList remove NodeList set NodeList getNode NodeList indexOf NodeList size NodeList copy constructor NodeList clear NodeList finalize Net getNode Net getNodes Node getParents Node getChildren Node getRelatedNodes Net getRelatedNodes NodeList mapStateList Cases Sets of Findings see also Findings Net Net Net Net Net writeFindings readFindings retractFindings getFindingsProbability reviseCPTsByFinding
129. nverting an Equation to a Table As mentioned earlier all equations must be converted to tables before compiling a net or doing net transforms like absorbing nodes or reversing links The procedure is done by the following three steps 1 If the node or any of its parents is a continuous node that has not yet been discretized then call Node setLevels to discretize it The finer the discretization the more accurate but the bigger the tables will be 2 If the node doesn t already have its equation call Node setEquation passing in the equation string 3 Finally call Node equationToTable Note that if you later change the equation for the node or the discretization of the node or of any of its parents or the finding of a constant node referred to by the equation you must repeat this step before the changes will take effect With the parameters passed to this function you can control the number of samples in any Monte Carlo integration that is required whether the final CPT will include uncertainty due to the sampling process and you can blend tables with those produced by learning from data other equations or manual CPT entry into Netica Application If Netica reports errors in the above steps it is often helpful to debug the equation using Netica Application If there is a problem with the syntax of an equation when you enter it into Netica Application s node property dialog box the cursor will be placed on the pr
130. nvironmental model you can determine which parts of the model most affect the variables of interest thereby identifying which parts should be made the most carefully and accurately Say you are interested in the beliefs of a particular node which we call the target node Then there are a set of other nodes called the varying nodes for which it may be possible to have findings and you want to know how much those findings are likely to influence the beliefs of the target node To use Netica s sensitivity functions you first create a Sensitivity object using the constructor Sensitivity Node targetNode NodeList varyingNodes int whatFind You pass it the target node targetNode and a list of the varying nodes varyingNodes You will be able to use the Sensitivity object returned to find the sensitivity of targetNode to each of the nodes in varyingNodes You also pass whatFind to indicate what type of sensitivity calculations you wish it to be able to perform which should be VARIANCE_OF_REAL_SENSV if you wish to be able to call getVarianceOfReal ENTROPY_SENSV if you wish to be able to call getMutualInfo or their bitwise or to be able to use both Finally you obtain the actual sensitivity numbers by calling one of these methods on the Sensitivity object double getMutuallnfo Node varyingNode double getVarianceOfReal Node varyingNode If the target node is discrete with no real number levels associated with the states then the
131. o X1 Xn nearest0 1 val Co Cy gt Cy select0 1 index Co Ci Cy member elem Si So Sn factorial n logfactorial n gamma x loggamma x beta z w erf x erfc x binomial n k multinomial n No Ny Continuous Probability Distributions UniformDist x a b TriangularDist x m w Triangular3Dist x m Wi w2 TriangularEnd3Dist x m a b NormalDist x u oO LognormalDist x n 6 ExponentialDist x dA GammaDist x a WeibullDist x a BetaDist x a Beta4Dist x a B c d CauchyDist x u LaplaceDist x u f ExtremeValueDist x u ParetoDist x a b ChiSquareDist x v StudentTDist x v FDist x Vir v2 JAVA VERSION 4 18 NETICA API 95 Discrete Probability Distributions SingleDist k c DiscUniformDist k a b BernoulliDist b p BinomialDist k n p PoissonDist k m HypergeometricDist k n s N NegBinomialDist k n p GeometricDist k p sogarithmicDis MultinomialDis bc nr ky Par Kor Por Kur Pm NoisyOrDist e leak bi Pi Do Po Day Pn NoisyAndDist e inh bi Pi Do Po Dnr Pn NoisyMaxTableDist NoisySumTableDist 11 12 Special Math and Distribution Functions Reference Legend lil Discrete Probability Distribution the first argument is a discrete variable that the distribution is over
132. o a query so can be pruned away This section deals with junction trees see the Modifying Nets chapter 22 NETICA API JAVA VERSION 4 18 for information on link reversals and node absorption Sampling is an inexact method and is usually used only when the Bayes net is too large to compile into a junction tree or there are continuous variables whose value you want to provide by equation and don t want to discretize It is accomplished by calling Net generateRandomCase many times say 1000 with argument method 2 FORWARD_SAMPLING and recording what percentage of the cases resulted in the node of interest having a given value Netica uses the fastest known algorithm for exact general probabilistic inference in a compiled Bayes net which is message passing in a junction tree or join tree of cliques This is based upon the work of LauritzenSpiegelhalter88 which is described in much simpler and more extensive terms in CowellDLS99 and SpiegelhalterDLC93 In this process the Bayes net is first compiled into a junction tree The junction tree is implemented as a large set of data structures connected up with the original Bayes net but invisible to you as a user of Netica You enter findings for one or more nodes of the original Bayes net and then when you want to know the resultant beliefs for some of the other nodes belief updating is done by a message passing algorithm operating on the underlying junction tree It determines the r
133. oblem while the error message is displayed From Netica Application s menu you can choose Equation To Table to check if there is going to be any problem with the equation and conveniently view the resulting CPT to see if it is what you expect 11 5 Equations and Table Size The size of the table generated is the product of the number of states of the node with the numbers of states of each of its parent nodes So if a node has many states or many parents then the tables may be very large and Netica may report that it doesn t have enough memory for the operation You can alleviate the problem by eliminating unnecessary parents introducing intermediate variables or using more course discretizations perhaps have more than one node for the same variable with different discretizations depending on which node it is a parent for If Netica creates extremely large tables it may starve other processes of memory or result in very slow virtual memory hard disk activity so you might want Netica to instead just report that it doesn t have enough memory In that case you can limit the amount of memory available to Netica with Environ setMemoryUsageLimit JAVA VERSION 4 18 NETICA API 89 11 6 Link Names In the simplest way of writing equations the names of the parent nodes appear in the equation However you might want a more modular representation so that you can disconnect some of the parent nodes and hook the node up to new
134. ode 50 setKind Node 60 90 in use 68 setMaxIterations Learner 54 setMaxTolerance Learner 54 in use 54 setNumber User 80 setObject User 80 setPassword Streamer 32 setRealFuncTable Node in use 68 setReference User 80 sets of findings functions available 107 sets of nodes 77 setStateNames Node 30 in use 68 setString User 80 sign eqn function 103 SimulateCases java example program 38 SimulateCases java file 10 simulation 83 single distribution eqn function 103 SingleDist eqn function 103 Snedecor distribution eqn function 98 soft finding 34 See also likelihood finding in case file 47 spreadsheet program 36 SQL Server MS database 40 src directory 11 src neticaEx aliases directory 18 standard normal eqn function 102 state name 37 statistics of net 56 stopping criterion for learning 48 NETICA API JAVA VERSION 4 18 Streamer class 105 structural relations between nodes 80 structure learning 46 student t distribution eqn function 103 StudentTDist eqn function 103 style of nodes 61 subtract passed to getRelatedNodes 79 support email address 13 switchParent Node 62 in use 63 system functions available 105 T tab delimited text file 36 table too big 88 tables functions available 110 target node 46 64 82 target node sensitivity 82 templates 20 termination condition
135. ode s value or CPT as a function of its parent nodes Builds the node s function or CPT table from its equation Defines a name for a link to be used by the node s equation instead of the parent node s name Calculates if possible the state of a node based on its deterministic equation or table and findings at its neighbor nodes Calculates if possible the numerical value of a node based on its deterministic equation or table and findings at its neighbor nodes The conditional probability of the node given its parent s values Experience quantities indicating how much data was used to learn each row of the CPTable Function table of a discrete deterministic node Function table of a continuous deterministic node Removes a node s function probability and experience tables Whether the node has a CPT table or function table Discovers if the node is a deterministic function of its parents Useful for getting states in correct order to access a table Builds table from equation Performs learning of CPT tables from data Modify CPTs by learning from a single case Modify CPTs by learning from cases Increase uncertainty in CPT table to account for passage of time Adds the given node to the node set of the given name Removes the given node from the node set of the given name JAVA VERSION 4 18 NETICA API 111 Node isInNodeset Returns whether the given node is a member of the given node set Net getAllNodesets Returns a li
136. of each of these words is also acceptable and does the same thing You can add certain modifiers in any order to the string containing the relation The allowed modifiers are append means to add to the list that is passed in otherwise that list is first emptied union means to add to the list that is passed in and remove all duplicates intersection means to reduce the passed in list to only the nodes that are in both the original passed in list and the relation subtract means to take the nodes that are in the relation away from the passed in list exclude_self is only relevant for ancestors descendents connected and d_connected Without it the relation list will also include the original node generation 0 include_evidence_nodes is only relevant for markov_blanket and d_connected Without it the relation list will not contain any nodes with findings For example to create a list of all the nodes that are both ancestors of node_A and descendents of node_B you could use 80 NETICA API JAVA VERSION 4 18 NodeList ad new NodeList net node_A getRelatedNodes ad ancestors node_B getRelatedNodes ad intersection descendents If you want to find all the nodes that are related to a whole group of nodes you use Net getRelatedNodes It works the same as Node getRelatedNodes except that it takes a list of nodes as an extra parameter void getRelatedNodes NodeList relatedNodes
137. on index Xingex The first x argument is at index 0 if selectO is used and at index 1 if select1 is used Must be passed at least 2 arguments index and an x See also member Example selectO 1 6 6 1 26 3 4 returns 3 4 selectl 1 6 6 3 4 3 4 1 26 returns 6 6 JAVA VERSION 4 18 NETICA API 103 sign x x gt 0 1 x lt 0 1 0 where x is an unrestricted real Returns 1 if x is positive 1 if x is negative and 0 if x is zero See also abs SingleDist k c lulu k c 1 0 Required k and c are integers The single point distribution indicates that k c The probability that k is any other value is 0 This is the discrete version of a Dirac delta StudentTDist x v laJ T v 1 2 sqrt v pi T v 2 14x 2 v v41 2 Required v gt 0 The t distribution or Student s t distribution arises in the problem of estimating the mean of a normally distributed population when the sample size is small TriangularDist x m w La x al gt w 20 w x al w Required w gt 0 The graph of this distribution has a triangular shape with the highest point at x a and nonzero values only from a w toa w Triangular3Dist x m w w2 La Required w gt 0 w gt 0 w amp w can t both be 0 The pdf has a triangular shape with the highest point at x m and nonzero value from m w to m w2 TriangularEnd3Dist x m a b La Required a lt m b gt m b gt a The pdf has a triangular shape with
138. ooth unimodal distribution on 0 1 can approximated to some degree by a beta distribution if its not on 0 1 see Beta4Dist Beta4Dist x a B c d La BetaDist x c d c a B Required 0 lt x lt 1 a gt 0 B gt 0 Also known as the Generalized Beta Distribution this is a beta distribution that has been shifted and scaled so that the pdf has nonzero values from x c to x d instead of from x 0 to x 1 This distribution has great flexibility to roughly fit almost any smooth unimodal distribution with no tails i e only nonzero over a finite range binomial n k n k n k Where 05k lt n n and k are integers Returns the binomial coefficient n k That is the number of different k sized groups that can be drawn from a set of n distinct elements See also the multinomial function BinomialDist is the binomial probability distribution which is based on the binomial coefficient BinomialDist k n p Lalli binomial n k p 1 p Required k and n are integers 0S k Sn and O0S pS81 A binomial experiment is a series of n independent trials each with two possible outcomes often labeled success and failure with a constant probability p of success The total number of successes k is given by the binomial distribution JAVA VERSION 4 18 NETICA API 97 If there are more than two possible outcomes use the multinomial distribution MultinomialDist Ifthe sampling is without
139. or you can leave that to the JVM JAVA VERSION 4 18 NETICA API 83 Currently Netica s sensitivity analysis works only on Bayes nets and not decision nets You can also use Netica Application to do sensitivity analysis by choosing Network Sensitivity to Findings from the menu For more information on Netica s calculation of sensitivity contact support norsys com and ask for the Sensitivity document 10 5 Stochastic Simulation Netica can be used to generate random cases aka synthetic data which are cases whose values follow the distribution represented by the Bayes net including any findings that it has This synthetic data may be browsed by people to get a feel for the type of cases to expect or used to test people on their predictive or diagnostic ability It can be used to learn other Bayes nets or other machine learning representations such as neural nets decision trees or decision rules Perhaps its most valuable use is when the Bayes net is a physical model of a real world situation and the synthetic data provides stochastic simulations The output of those simulations can then be analyzed by other programs For example the Bayes net may model a warehouse and distribution scheme which can be tested under various conditions to check its performance In a similar vein the Bayes net may model a control system economic system political environment computer network etc To generate a synthetic cas
140. otentially extend to infinity but in practice will be limited by known maximum values for the variable Likelihood within the interval is one outside the interval it is zero Set of Possibilities Syntax Siz Soy a Sal each s is a state name state index preceded by Gaussian interval or unbounded interval Examples lo med red blue yellow 5 7 1 POy3 5 5 EASy 10 4 35 122 gt 500 This finding indicates the value is known to be one of a listed set of possibilities There may be spaces before or after the comma or brackets The finding can be considered to be a disjunction of the elements So if there is only 1 element x the value is known to be that element and it can be written as just x The likelihood of elements in the set is one of those not in the set is zero 44 NETICA API JAVA VERSION 4 18 Set of Impossibilities Syntax Si S2 Sn each si is a state name state index preceded by interval or unbounded interval Examples 1lo black orange green 5 7 1 SE LOG 3o5 4 This finding indicates the value is known to not be any of a listed set of possibilities There may be spaces before or after the comma or braces but not between the tilde and the brace This is the same as Set of Possibilities except the possible states are those that are not listed rather than those that are listed The likelihood of elements in the set is zero of those not in the set it is one
141. parents without having to change all the parent names within the equation Or perhaps you duplicate the node to use with new parents Or you put the node in a network library without any parents Or you want to copy the equation from one node to another without changing all the node names The way to do that is to use input names sometimes called link names They provide an argument name for each link entering the node and therefore a proxy for each parent node You can set them with Node setInputName You refer to them in your equation in exactly the same way you would the corresponding parent name When a parent is disconnected the link name will remain Note If link names are defined for a node they must be used instead of the parent names 11 7 Referring to States of Discrete Nodes To refer to the states of a discrete or discretized node You can use the state names of a discrete node as constants in an equation For example if node Color has states red green blue and yellow and node Temperature has states cool and warm you could write Temperature Color member Color red yellow warm cool Each state name only has meaning relative to the node it s for Usually when you use a state name Netica can identify that node from context However if Netica doesn t know which node a state name refers to e g it gives an unknown value error message you can indicate which node by following the state name with a double
142. r then during usage Netica won t know the value of the class variable If the net is to be used for prediction then Netica won t know the values of the variables that are yet to occur in time If the net is to be used for diagnosis Netica won t know what the actual faults or internal states are during the diagnosis The variables i e nodes that will not be known during usage are called the unobserved nodes The next step is to choose which of the unobserved nodes you want to test the Bayes net s ability on These are the nodes that statistics will be generated for and are called the test nodes In the code you first call new NetTester passing in a list of the test nodes If there are some unobserved nodes that aren t already in the test nodes you pass in a list of them as the unobsv_nodes argument which can also include any of the test nodes if you want it makes no difference since Netica will take as the unobserved nodes the union of the two lists Then you call Tester testWithCaseset passing in the case file containing the real world data Netica will go through the case file processing the cases one by one Netica first reads in a case except for findings for the unobserved nodes It then does belief updating to generate beliefs for each of the test nodes and checks those beliefs against the true value for those nodes as supplied by the case file if they are supplied for that case It accumulates all the compar
143. replacement use the hypergeometric distribution HypergeometricDist For large n and p not too close to 0 or 1 the binomial distribution can be approximated by a normal distribution NormalDist with mean m n p and variance n p 1 p For large n and p close to 0 it can be approximated by a Poisson distribution PoissonDist with parameter n p As n these are the limiting distributions providing p constant in the normal case and p 0 np constant in the Poisson case CauchyDist x u o MA 1 7 0 1 poy Required o gt 0 Although real world data rarely follows a Cauchy distribution it is useful because of its unusualness For example although it is symmetric about p which is therefore its median and mode it doesn t have a mean or variance etc because the appropriate integrals don t converge The C 0 1 distribution is also Student s t distribution with degrees of freedom 1 ChiSquareDist x v La x exp x 2 2 gamma v 2 Required x 2 0 v gt 0 v is an integer This is the distribution of Z Z Z where Z are independent standard normal NormalDist variates v is usually called the degrees of freedom of the distribution clip min max x x lt min min x gt max max x where min lt max Returns x unless it is less than min in which case it returns min or more than max in which case it returns max See also the functions min max DiscUniformDist
144. robability of the next ball being white should be less than 0 5 because you know that now there are more black than white balls in the bag 10 black and 6 white One way to handle this using just probabilities is to keep track of your beliefs about the ratio of white to black balls in the bag Then you will have many probabilities one for each possible ratio Each of these probabilities will change as you draw a ball and when you are asked to supply a probability that the next ball drawn will be white they will all be involved in the calculation This is sometimes called second order probabilities but here it is really just a probability distribution over possible ratios If you discretized the possible ratios then it would be easy to set up a Bayes net for this with the ratio being one of its nodes That approach works fine for this simple problem but you can imagine that if you had many interrelated variables that it could become too cumbersome If during the learning we consider the conditional probabilities being learned to be independent of each other and the prior distribution to be Dirichlet then we can use beta functions to represent the distributions over probabilities Each beta function requires 2 parameters to be fully specified and Netica uses a probability number and an experience number This way true Bayesian learning of the probabilities is easy to do since it is easy to express how the beta function should change to account
145. rst covers all cases where B lt 2 the second covers cases 2 lt B lt 6 and the last covers the remaining cases i e B 2 6 So if B is less than 2 X is distributed normally with mean 3 Y if it is between 2 and 6 then the mean is 2 Y and if it is over 6 then X is distributed uniformly If there are more parents this sort of construct can be nested to provide a tree structure of possible contingencies Here are a couple more examples They show a way to condition over the states of a discrete node p X B B yellow NormalDist X 2 sqrt Y B orange NormalDist X 4 Y B red NormalDist X 6 Y 2 0 p X B member B CA TX FL NormalDist X 3 1 member B MA WA NormalDist X 5 1 member B NY UT VA NormalDist X 7 2 UniformDist X 0 10 Notice that the fall through case of the first example above is simply a 0 This indicates that the designer is counting on B to be one of yellow orange or red If B ever has another state then when Netica is converting the equation to a table it will give a warning message that for n N conditions no nonzero probability was discovered by sampling providing no sampling uncertainty is being added In the last example the fall through case gives a uniform distribution If extra states are later added to B then they will just fall through and use the uniform distribution 88 NETICA API JAVA VERSION 4 18 11 4 Co
146. rsys com resources htm Bayes Net Library A website containing many example Netica files that are ready to download into Netica Application or API They are Bayes nets and decision nets that have become classics in the literature or are contributed by other Netica users This is a good place to look for inspiration and ideas Website location http www norsys com net_library htm DNET File Format Describes the file format for Netica DNET files which have file extension dne or dnet Website location http www norsys com dl DNET_File_Format txt JAVA VERSION 4 18 NETICA API 15 2 Netica J Package Design and Usage This section outlines programming principles and issues as they relate to Netica J s operation and organization If you are an experienced Java developer or you are planning a sizeable development effort with Netica J you will definitely want to read and understand this section before beginning your development 2 1 The Ex classes NetEx NodeEx and NodeListEx The Ex classes inherit from their parent class NodeEx extends Node NetEx extends Net etc They are built on top of the core Netica system to provide convenience of use the Ex stands for Extra Example External Experimental and Excellent These are utilities and shortcuts that were deemed useful but not basic enough to belong in the base class Some of them are Ex methods
147. s NETICA API 107 Reads a file of cases to revise each node s probabilities Uses the current case to revise probabilities Creates a new object for use in learning CPTs from case data Deletes a learning object learner Learn CPTs from case data with choice of algorithm The maximum number of learning step iterations i e complete passes through the data which will be done when the learner is used The minimum change in data log likelihood between consecutive passes through the data as a termination condition Adjusts a node s probabilities for a changing world Returns the results of learning Determines how much experience was involved in the learning Directly sets the probabilities or starts them off Manually sets the amount of experience or starts it off Returns the expected utility of each choice in a decision node Used to create decision nodes and utility nodes Creates a new empty list of nodes Inserts a node at the given position of a list making it one longer Removes the node at the given index of a list making it one shorter Sets the Nth node of a list to a given node without changing length Returns the Nth node of a list the first node is numbered 0 Returns the position index of a node in a list or 1 if it is not present Returns the number of nodes in a list Duplicates a list of nodes Empties a node list without releasing the memory it uses Frees the memory used by a list of nodes Returns the node with th
148. s to come Netica API features e Dynamic Construction Can build and modify networks on the fly in memory to support working with dynamic Bayes nets and can save read them to file e Equations Probability tables may be conveniently expressed by equations using a Java C type syntax and taking advantage of an extensive library of built in functions including all the standard math functions and common probability distributions as well as some functions and distributions specially suited to Bayes nets such as noisy or noisy max noisy sum etc e Learning from Data Probabilistic relations can be learned from case data even while the net is being used for probabilistic inference Learning from data can be combined with manual construction of tables and representation by equations It can handle missing data and latent variables or hidden nodes Learning algorithms include counting sequential updating fractional updating EM expectation maximization and gradient descent e Database Connectivity Allows direct connection to most database software e Threadsafe Can be used safely in multi threaded environments e Encryption Can save and read nets to file in encrypted form which allows deploying solutions relying on Bayes nets kept private to an organization 8 NETICA API JAVA VERSION 4 18 e Sensitivity Netica can efficiently measure the degree to which findings at any node can influence the beliefs at another node given t
149. s possible then generate an error explaining exactly why it was impossible to proceed JAVA VERSION 4 18 NETICA API 67 8 Decision Nets Chapter 3 was about probabilistic inference using a Bayes net where the purpose was to determine new beliefs in the form of probabilities as observations were made or facts gathered A Bayes net is composed only of nature nodes which may be chance nodes or deterministic nodes By adding decision nodes and utility nodes also known as value nodes to a Bayes net we obtain a decision net also known as an influence diagram Decision nets can be used to find the optimal decisions which will maximize expected utility First we give a small warning You may find it overly challenging if your first usage of Netica API is to build a large decision net with multiple decisions and you haven t had related experience People usually start by building Bayes nets then nets with just one decision and after they have some experience nets with a few decisions Also they usually have some experience working with nets using Netica Application or a similar program before using Netica API for complex decision nets As an example decision net let s consider a very tiny one from Ross Shachter known as Umbrella It has 2 nature nodes representing the weather Forecast in the morning sunny cloudy or rainy and what the Weather actually turns out to be during the day sunshine or rain a
150. scent learning then if you wish you can adjust the stopping conditions with void setMaxlterations int maxlterations void setMaxTolerance double logLikelihoodTolerance Finally you perform the learning with void learnCPTs NodeList nodeList Caseset caseset double degree by passing in the nodes whose CPTs you wish to modify the data as a Caseset see the previous chapter for instructions on creating a Caseset and the degree which is a multiplier for the frequency of the cases e g degree 3 means act as if every case in the Caseset appeared 3 times When you are done with the Learner you may reduce the resources required by calling void finalize Here is a small code example for another see Connecting with a Database in the previous chapter Streamer netfile new Streamer ParameterlessNet dne JAVA VERSION 4 18 NETICA API 55 Streamer datafile new Streamer Data cas Net net new Net netfile env no_ visual NodeList nodes net getNodes Caseset cases new Caseset Learner learner new Learner Learner EM_LEARNING learner setMaxTolerance 1e 5 cases addCases datafile 1 0 null learner learnCPTs nodes cases 1 0 learner finalize cases finalize 6 7 Fading When a Bayes net is supposed to capture relationships between variables in a world which is constantly changing it is useful to treat more recent cases with a higher weight than older ones An example mi
151. st of all node sets defined for this net in priority order Net reorderNodesets Re orders the node sets as requested for priority during display Net g setNodesetColor Gets or sets the color used to display nodes of a given node set Visual Display See also the NetPanel and NodePanel classes Node visual g setStyle The style to draw the node in Netica Application Node visual g setPosition The coordinates of the center of the node in the Netica Application User Data Fields These are also all repeated for the Net object Node user g setNumber Attaches a named field number to the node that gets saved to file Node user g setString Attaches a named field string to the node that gets saved to file Node user g setObject Attaches a named field Serializable object to the node that gets saved to file Node user g setBytes Attaches a named field blob to the node that gets saved to file Node user removeField Removes one of the named fields of the node Node user getNthFieldName Retrieves field by field info from the node by index Node user g setReference Attaches a single arbitrary data object to the node not saved to file 112 14 Index Symbols for state index 37 in case file 37 in UVF file 45 in case file 37 a b in UVF file 43 _ Bernoulli Function eqn function 96 in UVF file 43 44 in UVF file 44 45 gt CASE 1 gt 37 in UVF file 42 gt in UVF file 43
152. stClinic dne net finalize catch Exception e e printStackTrace This alternate way can replace the net reviseCPTsByCaseFile line above if you need to filter or adjust individual cases long casePosn new long 1 casePosn 0 Net FIRST_CASE while true 54 NETICA API JAVA VERSION 4 18 net retractFindings net readFindings casePosn caseFile nodes null null if casePosn 0 Net NO_MORE_CASES break net reviseCPTsByFindings nodes 1 0 casePosn 0 Net NEXT_CASE 6 6 EM and Gradient Descent Learning As described in the Algorithms section above counting learning should be done when possible because it is much faster and simpler but in cases where there is a substantial amount of uncertain findings missing data or even variables for which there are no observations EM or gradient descent learning can do amazing things If you are unfamiliar with the nature of these learning algorithms you may first want to experiment with them on your data a little using Netica Application and read its onscreen help about EM learning The below method can be used to do any of Netica s learning algorithms First you create a Learner by calling Learner int method String info Environ env passing for method the algorithm you wish to use one of Learner COUNTING_LEARNING Learner EM_LEARNING or Learner GRADIENT_DESCENT_LEARNING If you are doing EM learning or gradient de
153. struction so that Netica J can do its own housekeeping upon the Java object being collected For example if your class extends norsys netica Streamer and you need to override the finalize method to perform special close down handling of files and such then your finalize method would look something like this overrides Streamer finalize public void finalize throws NeticaException your own finalization logic super finalize 20 NETICA API JAVA VERSION 4 18 3 Probabilistic Inference 3 1 Bayes nets and Probabilistic Inference A Bayes net also known as a Bayesian network BN BBN belief network probabilistic causal network or graphical model captures our believed relations which may be uncertain or imprecise between a set of variables that are relevant to some problem They might be relevant because we will be able to observe them because we need to know their value to take some action or report some result or because they are intermediate or internal variables that help us express the relationships between the rest of the variables Some Bayes nets are designed to be used only once for a single world situation More often Bayes nets are designed for repetitively occurring situations They may be constructed using expert knowledge provided by some person by an automatic learning process which examines many previous cases or by a combination of the two If the net is to be used repetitively th
154. t already had nodes that correspond to columns of the database to form the nodeList parameter for them If it doesn t then you can create the nodes with void DatabaseManager addNodes Net net String columns String tables String condition String control When you are done with the database manager you may close the connection and free resources by calling void DatabaseManager finalize Here is an example program to learn Bayes net CPT tables from a database For more explanation on learning see the next chapter and especially a similar code example in the EM and Gradient Descent Learning section DatabaseManager db new DatabaseManager driver Microsoft Access Driver mdb dbg myDB mdb UID dba1 pooling env Net net new Net Put code to add nodes and links to net here 42 NETICA API JAVA VERSION 4 18 You could use DatabaseManager addNodes NodeList nodes net getNodes Caseset cs new Caseset cs addCases db 1 0 nodes Sex Height Owns a house Number of dogs null Owns a house yes null Learner learner new Learner Learner EM_LEARNING null env learner learnCPTs nodes cs 1 0 cs finalize db finalize 5 4 Case Files with Uncertain Findings The case files discussed so far have only had values that were completely certain or completely missing But Netica can also create and read case files having values that
155. t comes from some node to come from a different node without changing the child node or its tables Sets the link s name to be used by the child node in its equation Attaches a callback for when nodes get created removed etc See also Equations Tables Node Sets Visual Display and User Data Fields Net Environ Node Node Node getName getTitle getComment getNodes getNode getFileName getAutoUpdate getElimOrder getNthNet getNet getName getTitle Returns the name of the net Returns the string which is the net s title Returns the comment associated with the net Returns a list of all the nodes in a net Returns the node having the given name from the net Name of file with full path that net was last written to or read from Returns whether the net does belief updating immediately Returns a list of the elimination order used for compiling triangulation Can be used to return all the nets in the Netica Environ one by one Returns the net containing the given node Returns the name of the given node Returns the string titling the node 110 Node getComment Node getType Node getKind Node getNumStates Node state getName Node state getIndex Node state getTitle Node state getComment Node state getNumeric Node getLevels Node getInputIndex Node getParents Node getChildren Node isRelated Node getRelatedNodes Net getRelatedNodes Equations
156. t if it is not able to do so it will ignore that information 9 2 Node Position If a Netica file has been saved without visual information then all of the Nodes are by default given a position of 0 0 To add position information you may use the Netica Application to display the net and then position the Nodes as desired or from within the Java API you may use Node visual setPosition Once a NodePanel has been created it is a Java component that can be moved anywhere e g using java awt Component setLocation without affecting the Node visual position data If you want to keep the displayed position in sync with the Netica visual position you must either manage this yourself or else confine yourself to moving the component by calling NodePanel moveBy 9 3 Node Style If a Node does not contain any style information introduced using Netica Application or by calling Node visual setStyle then Netica J will apply certain default styles when creating NodePanels NodePanel createNodePanel for that node Conversely if the node does contain style information that information will be treated as the preferred style when Netica J is given an option in deciding what variety of NodePanel to create JAVA VERSION 4 18 NETICA API 75 9 4 Drawing Nodes You do not require the NetPanel class to draw nodes You may draw the nodes directly using any of several NodePanels that are supplied Circle Absent Belief
157. te 1 Steps 4 and 5 enter another likelihood finding and then step 6 retrieves the likelihood vector for the accumulated findings so far It will have the values clike 0 0 3 clike 1 0 0 clike 2 0 0 clike 3 0 5 36 NETICA API JAVA VERSION 4 18 Notice that clike 1 is 0 due to the negative finding of step 3 and clike 2 is 0 due to the 0 in the likelihood finding of steps 4 amp 5 Step 7 is commented out but if it weren t it would generate an error because saying the value of node is state 2 is inconsistent with the likelihood finding of steps 4 amp 5 Step 8 causes a belief updating to be done and it could return a belief vector with the following values belief 0 0 9 belief 1 0 0 belief 2 0 0 _ belief 3 0 1 Even though the accumulated likelihood clike said state 3 was the most likely value for node when the findings for other nodes and their relations with node were taken into account state 0 became more probable than state 1 In general it is not possible to determine anything about what the belief of a node is going to be based just on its accumulated likelihood findings except that states with a zero likelihood will have a zero belief Step 9 demonstrates getState being used to query what finding has been entered for node It is designed to retrieve positive findings and since node has likelihood findings it will just return the constant Value LIKELIHOOD_VALUE Step 10 retracts all the findin
158. te approach Finally the program concludes by saving the new net to file so that we can compare it with the old It will be similar but the probabilities won t be quite the same The more cases we put in the case file the more similar the learned net will be to the original Of course in a real application there would be no point in relearning a net which already existed you would use a case file that had real cases in it But this demonstration is good to show that the new net comes out similar to the old Vhs LearnCPTs java Example use of Netica J for learning the CPTs of a Bayes net from a file of cases import java io File JAVA VERSION 4 18 NETICA API 53 try import norsys netica public class LearnCPTs public static void main String args Environ env new Environ null Read in the net created by the BuildNet java example program Net net new Net new Streamer Data Files ChestClinicBuilt dne NodeList nodes net getNodes int numNodes nodes size I Remove CPTables of nodes in net so new ones can be learned for intn 0 n lt numNodes n Node node nodes getNode n node deleteTables Read in the case file created by the SimulateCases java Il example program and learn new CPTables Streamer caseFile new Streamer Data Files ChestClinic cas net reviseCPTsByCaseFile caseFile nodes 1 0 net write new Streamer Data Files Learned_Che
159. tems as you wish to an object each under its own name i e attribute value Your data will be duplicated if the node is duplicated and when you save your net to file Netica will include your data in the file Representative prototypes are void setNumber String fieldName double fieldValue void setString String fieldName String fieldValue void setObject String fieldName java io Serializable fieldValue void setBytes String fieldName byte bytes JAVA VERSION 4 18 NETICA API 81 void removeField String fieldName double getNumber String fieldName String getString String fieldName Object getObject String fieldName byte getBytes String fieldName String getNthFieldName int index To set a user field you pass a name for the field and a reference to your data When you later call the method to recover your data you pass in the name you gave it and Netica will return you a newly constructed object identical to the original except for its hashcode For example myNode user setString author Sarah String author myNode user getString author User fields can be very conveniently viewed or modified using Netica Application which provides a good way of transferring information between an end user and your Netica J program as are node sets If you wish to find all the user fields defined for some node or net you can iterate through them with User getNthFi
160. the cases are learned sequentially through time then the amount of fading to be done is degree 1 r t where At is the amount of time since the last fading 56 NETICA API JAVA VERSION 4 18 was done and r is a number less than but close to 1 and depends on the units of time and how quickly the environment is changing Different nodes may require different values of r See the example in the description of fadeCPTable in the Function Reference chapter 6 8 Performance Testing a Net using Real World Data After you have built a Bayes net either by hand based on the judgments of an expert or automatically by learning it from data you may want to test how effective it is That can be done by using a set of cases gathered from the real world or from the environment in which the net will be used You should use a different data set than was used to build the Bayes net otherwise your net may score too high since it will probably test slightly better on the training set than other sets A common approach when learning a Bayes net from data is at the beginning to set aside a certain percentage of the well shuffled cases to be used for later testing These are known as the test cases or test data as opposed to the training cases or training data The first step is to identify the variables i e nodes that Netica won t know the value of during actual usage of the net For example if the net is to be used as a classifie
161. the highest point at x m and nonzero value from a to b UniformDist x a b La 1 b a Required a lt b This is the distribution to use when the minimum and maximum possible values for a variable are known but within that range there is no knowledge of which value is more likely than another It has a constant value from x a to x b and zero value outside this range WeibullDist x a B MA a B x B exp x B Required a gt 0 B gt 0 The Weibull distribution is often used for reliability models since if the failure rate of an item i e percent of the remaining ones which fail as a function of time is given as Z t r t t then the distribution of item lifetimes is given by the Weibull distribution with r a B xor bi bo Dn odd NumberTrue bj by b where b are boolean Returns the exclusive or of by bz By This is also known as the parity function and will return true iff an odd number of b evaluate to true See also and or not 104 NETICA API JAVA VERSION 4 18 12 Bibliography Russell Stuart and Peter Norvig 1995 Artificial Intelligence A Modern Approach Prentice Hall Pearl Judea 1988 Probabilistic Reasoning in Intelligent Systems Networks of Plausible Inference Morgan Kaufmann San Mateo CA Lauritzen Steffen L and David J Spiegelhalter 1988 Local computations with probabilities on graphical structures and their application to expert systems
162. the words node and variable are used interchangeably throughout this manual but variable usually refers to the real world or the original problem while node usually refers to its representation within the Bayes net The nodes are then connected up with directed links Usually a link from node A the parent to node B the child indicates that A causes B that A partially causes or predisposes B that B is an imperfect observation of A that A and B are functionally related or that A and B are statistically correlated The precise definition of a link is based on conditional independence and is explained in detail in an introductory work like RussellNorvig95 or Pearl88 Finally probabilistic relations are provided for each node which express the probability of that node having different values depending on the values of its parent nodes After the Bayes net is constructed it may be applied For each variable we know the value of we enter that value into its node as a finding also known as evidence Then Netica does probabilistic inference to find beliefs for all the other variables Suppose one of the nodes corresponds to the variable temperature and it can take on the values cold medium and hot Then an example belief for temperature could be cold 0 1 medium 0 5 hot 0 4 indicating the probabilities that the temperature is cold medium or hot The final beliefs are sometimes called posterior probabilities with prior
163. thod to be non static or vice versa should you prefer the alternate Because the Ex classes are so useful many developers will want to use them directly To make this easy their compiled classes have been included in the NeticaJ jar distribution All you need do is import norsys neticaEx and you are ready to use them without the need to compile your own versions of them Finally as a convenience we also supply in the norsys neticaEx aliases package three wrapper classes for NetEx NodeEx and NodeListEx that are named Net Node and NodeList respectively They allow you to use the base class names and still use the Ex classes See demo Demo java and examples BuildNet java for examples of how to use these convenience classes 2 2 Inheritance of the Node and Net classes Advanced users will want to create their own specialized Node and Net classes To make this task easier and avoid the need for copy constructors we have supplied you with a means to inform Netica J what class you would like it to use when constructing a Net or Node for example when Netica J is reading a net in from a file The static methods Net setConstructorClass String className and Node setConstructorClass String className have been supplied for this purpose All they require is that your Net or Node extension have a default constructor See their javadocs pages for examples Some users will want to use the words Net and Node
164. tic causal models 6 probabilistic causal network 20 probabilistic equation 85 probabilistic inference 21 by node absorption 65 example program 22 probability as a measure of uncertainty 49 probability revision 21 Prolog 6 Q quadratic loss 57 quality assurance 7 question finding best 82 questions email address 13 R random case generation 83 readFindings Net 42 in use 52 reduction in entropy 82 referring to discrete states in equation 89 regression testing 7 relations structural between nodes 80 removal of node callback 18 removeField User 80 reorderStates Node 60 resources for Netica 14 retractFindings Net in use 38 52 reverseLink Node 65 reviseCPTsByCaseFile Net 51 in use 52 118 reviseCPTsByFindings Net 51 52 right hand side of equation 86 risk analysis 7 round eqn function 102 roundto eqn function 102 run bat file 10 S sampling 22 second order probabilities 50 select0 eqn function 102 select1 eqn function 102 Sensitivity class 108 Sensitivity document 83 sensitivity to findings 81 functions available 108 Sensitivity constructor 82 sensor fusion 7 set of cases 40 set of impossibilities in UVF file 44 set of possibilities in UVF file 43 setBytes User 80 setConstructorClass Net and Node 16 setCPTable Node 30 in use 68 setCPTable NodeEx 30 setExperTable N
165. tic inference tasks Programs that use Netica J completely control it For example Netica functions will not take any action until called Netica will not do any I O unless requested to and its functions will not take an unpredictable amount of time or memory before returning Netica J is threadsafe in multi threaded environments It may be used in conjunction with other Java or JNI C libraries and it won t interfere with them Versions of Netica J are available for MS Windows Linux and Macintosh and for many other platforms from cell phones to mainframes contact us for info and each of these has an identical interface so you can move your code between these platforms without changing anything to do with the Netica API For the latest versions for the more common platforms visit http www norsys com download_api html Before releasing any new version of the Netica API every function is put through rigorous quality assurance testing to make sure it operates as designed Hundreds of real nets and millions of random nets are generated and solved in multiple ways to check the inference results This level of QA combined with a careful initial design and over ten years of extensive customer usage has resulted in a rock solid product The Netica API has been designed to be easily extended in the future without changing what already exists Many new features are currently under development and it will continue to be extended for year
166. tic loss result of the testing Creates a new database manager object for a given database Closes connection and deletes a database manager object Adds current findings within the net into the database as a new record Adds the cases or a subset in the database to a case set object Executes arbitrary SQL commands on the database Adds to the given net nodes that match the variables in the database Reverses a single link while maintaining joint probability Absorbs out sum or max some net nodes Builds a node s CPT or function table based on its equation Switches a link that comes from some node to come from a different node without changing the child node or its tables Duplicates each node in a list putting them in the same or a new net Duplicates a whole net with options to skip tables etc Undoes the last operation done to a net Call this to re do an operation that was undone JAVA VERSION 4 18 Low Level Net Modification NETICA API 109 See also Equations Tables Node Sets Visual Display and User Data Fields DatabaseManager Node Node Node Node Node Node Node Node Node Node Node Node Node Node Node Node Node Node Retrieving Net Information constructor finalize setName setAutoUpdate setElimOrder setTitle setComment addListener constructor delete duplicateNodes addNodes setName setTitle setComment setKind setStateNames state setName state
167. ts is not lost The disconnected link is given the name of the parent it once had if the link is not already named If you ever want to check whether a link is disconnected use Node getKindQ When you want to use something in the library you call Net copyNodes again this time to duplicate from the library into the new net Then you connect up any disconnected links with Node switchParent which will switch out the parent place holder and switch in the new parent Below is a code example for the flow measuring instrument described earlier Net net new Net Node flow new Node flow_rate 0 net Node temp new Node temperature 0 net Node broken new Node instrument_status 5 net Node instrument new Node instrument 0 net JAVA VERSION 4 18 NETICA API 63 instrument addLink flow instrument addLink temp instrument addLink broken M aia Put here Build probabilistic relation for node instrument either by learning from cases or entry by an expert Mass The below will put a copy of the instrument node disconnected from its parents into the library Its disconnected link names will be those of the old parents Net libnet new Net duplicate instrument libnet II see definition below libnet write new Streamer Library dnet net finalize libnet finalize II This is a static variant of NodeEx duplicate used above publi
168. tual evidence See also soft finding Visual Basic 6 NETICA API 119 visual display functions available 111 VisualNode class 111 WwW WARNING ERR 18 Weather example 61 Weibull distribution eqn function 103 WeibullDist eqn function 103 wild state reading case 37 Windows 7 working with findings functions available 106 write Net 31 32 in use 62 writeCases Caseset 40 writeFindings Net in use 38 X xor eqn function 103
169. u can refer to the value of a constant node anywhere in any node s equationby using the constant node s name It should not appear in the argument list on the left hand side of the symbol No link is required When you convert the equation to a table the value of any constant nodes it references will be used If you change the value of a constant node you must rebuild the table for the change to take effect 11 9 Tips on Using Equations e It is often helpful to debug equations using Netica Application If there is a problem with the syntax of an equation it leaves the cursor on the problem while it displays an error message You can choose Equation To Table from the menu to check that and easily view the resulting CPT to see if it is what you expected e The tables generated by equations may result in large files and therefore slow reading so you may want remove the nodes tables with Node deleteTables before saving it to file Later when you restore the net from file you call Node equationToTable to fully restore them e If you need to define intermediate variables to simplify the equations implement them as new intermediate nodes JAVA VERSION 4 18 NETICA API 91 11 10 Specialized Examples State Comparisons Suppose the states of node Source are CA TX FL BC and NY The states of node Dest are TX NY MA and UT We want to know if cross border travel is required to transport from Source to Dest and
170. ue may be given by a state name or state number but the continuous number is preferred if it is available That way the case file can be used for different discretizations of that variable in the future Try to use the correct number of significant figures since future versions of Netica may use this information A single case file is the same as one with multiple cases except it just has 1 case There may be as much whitespace as desired between the lines including Java C C style comments If the values of some of the variables are unknown for some of the cases then a question mark or asterisk or is put in the file instead of the value this is known as missing data If you read in a case and the case file has a node value that doesn t correspond to any state of that node in the net e g the states of net node color are red and green and the value for color in the case file is blue then an error will be generated An exception to this is if one of the states of the net node is called other Then the case will be read without error and the finding for the node will be other There are two special columns that a file may have which don t correspond to nodes One provides an identification number for each case which must be an integer between 0 and 2 billion The heading for this column is IDnum Identification numbers do not have to be in order through the file The other 38 NETICA API JAVA VERSIO
171. ugate gradient descent Both algorithms can get stuck in local minima but in actual practice do quite well especially the EM algorithm Most neural network learning algorithms such as backpropagation and its improvements are gradient descent algorithms That invites a comparison between Bayes net learning and neural net learning with latent variables corresponding to hidden neurons In the case of Bayes net learning there are generally fewer hidden nodes the learned relationships between the nodes are generally more complex the result of the learning has a direct physical interpretation by probability theory rather than just being black box type weights and the result of the learning is more modular parts can be separated off and combined with other learned structures 6 2 Experience There has been considerable controversy over the best way to represent uncertainty with some of the suggestions being probability fuzzy logic belief functions Dempster Shafer etc Currently probability and fuzzy logic are the most practical methods Of these two probability has a much sounder theoretical basis at least with respect to the way they are actually used However a deficiency of using nothing but probability is the inability to represent ignorance in an easy way As an example suppose you had to draw a ball from a bag full of black and white balls and you couldn t tell how many white balls and how many black balls there were in the ba
172. umulated findings for a node as a likelihood vector Returns what kind of finding was entered Retracts all findings for a single node Retracts all findings i e the current case from a net Returns the joint probability of the findings entered so far Compiles a net for fast belief updating Releases the resources e g memory used by a compiled net The size and speed of the compiled net i e of the junction tree Returns a string describing the internal compiled junction tree The node order used to guide compilation Automatically propagate beliefs when findings are entered Builds the CPT for a node based on the equation given to it Belief Updating and Inference Node Node Node Node Sensitivity Sensitivity Node Node getBeliefs getExpectedValue getExpectedUtils isBeliefUpdated g setAutoUpdate getJointProbability getFindingsProbability getMostProbableConfig generateRandomCase absorbNodes getMutualInfo getVarianceOfReal calcState calc Value Returns a node s current beliefs doing belief updating if necessary Expected value and std dev of a continuous or numeric valued node Returns the expected utility of each choice in a decision node Returns whether a node s beliefs have already been calculated to account for current findings Automatically propagate beliefs when findings are entered Returns a specified joint probability given the findings entered Returns the joint probability of the findings e
173. urce software that is distributed with Netica J You are free to examine compile or copy from these source files We suggest that you leave the original files unmodified These functions may change in future version of Netica The demo directory contains a simple program that should be compiled and run after installation to establish that your Netica J system is correctly installed and ready to use The examples directory contains assorted sample data and source code that you may examine copy and edit freely 1 4 Getting Started Recommended Installation steps 1 A Java 2 platform is required There are many suppliers for example SUN Microsystems at http java sun com products Version 4 18 was constructed using Java 1 4 2 and should be compatible with any 1 4 and higher platform 2 Download Netica J from the Norsys website http www norsys com netica j html older versions can be found at http www norsys com downloads old_versions Choose a version that matches your OS platform 3 Unzip it and it will form a directory called NeticaJ_325 or the current version number 4 Test your installation with the Demo application provided a Change to the demo directory and at the command line type compile bat compile sh on Unix Linux MacOSX Or click on the compile bat icon This will compile Demo java and create Demo class b At the command line type run bat run sh Or click on the run bat icon This
174. will run Demo class c Ifit displays a welcome message and does simple probabilistic inference without declaring any errors then your installation was successful 5 Now that you have the example program running you can duplicate the demo directory replace Demo java with your own source files and you are ready to build your own application Don t forget to replace null in new Environ null with your own license password if you want to have the full functionality of Netica 12 NETICA API JAVA VERSION 4 18 6 Demo java is a good starting point for developing your own applications You may wish to cut and paste from it Similar examples showing how to build a net from scratch do inference generate cases and learn from cases are provided in the examples directory 7 If you are familiar with the Hugin or JavaBayes systems and would like information on equivalent Netica functions contact Norsys 1 4 Complete Javadocs Reference For javadocs style documentation for Netica J simply point your browser at the index html file in the docs javadocs directory The javadocs very thoroughly document every class and every function of the Netica API You will find it an invaluable companion during development 1 5 IDE Installation Using Java IDEs Eclipse JBuilder NetBeans JDeveloper Forte etc You must inform your IDE of the locations of the three library files NeticaJ dll libNeticaJ so NeticaJ jar and
175. xt nodes In each of the queries you will be receiving new findings for 4 other nodes and then you want the resulting beliefs of the remaining 2 The nodes that will have new findings are called findings nodes and those whose beliefs you will want are called target nodes The hundreds of other JAVA VERSION 4 18 NETICA API 65 nodes in the net might be involved in intermediate calculations but you don t care about their values explicitly You can simplify the large net down to one with just 6 nodes using Net absorbNodes First enter the permanent findings for the context nodes Then make a list of all the nodes except the findings nodes and the target nodes and pass it to Net absorbNodes The resulting 6 node net will give the same inference results as the original large one for the restricted queries you will be making If you are guaranteed that there will always be findings for every findings node then you can then further simplify things by removing any links that go from findings node P to findings node C providing C does not have a target node as an ancestor This means that if you use Node reverseLink to make all the findings nodes ancestors of all the target nodes then you can remove all the links between the findings nodes Any findings node that is left completely disconnected by this operation is irrelevant to the query And now you can examine the conditional probability relations of the target nodes to see directly how they
176. you add cases to the Caseset If you want them to come from a database you use Caseset addCases DatabaseManager as described in the next section Alternatively you can add cases from a text file of cases in the format described in the previous section You first create a Streamer that refers to the file using new Streamer yourFile cas If you are creating the case file dynamically it is probably much more efficient to just create it in a memory buffer say a byte array and then create the new Streamer new ByteArrayInputStream CyourByteArray instead Then you add the cases within it to the Caseset using Caseset addCases Streamer streamer double degree String control With the current version of Netica you can only add cases to a Caseset once You can write all the cases in a Caseset to a file with Caseset writeCases Streamer file String control That can be used to extract the cases from a database and then write them out to a text file You can use Learner learnCPTs to learn the conditional probability tables of a Bayes net from a Caseset as described in the Learning chapter Future versions of Netica will have many more operations available for Casesets When you are done with the Caseset you may reduce the resources required by calling Caseset finalize 5 3 Connecting with a Database Netica can connect with a database such as that created by Microsoft SQL Server Microsoft Access MySQL or Oracle

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