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User's Guide - Norsys Software Corp.

1. 81 12 Equations The relation between a node and its parents can be entered using an equation if desired This is possible whether the nodes are continuous or discrete and whether the relation is probabilistic or deterministic Before inference Netica turns the equation into a table and uses the table in the same way as if you had entered it by hand as described in previous chapters For documentation on using the equation feature contact Norsys Software Corp by email at norsys_info norsys com 82 13 Bibliography Each bibliography reference is also listed in the index so you can find where in this document it is mentioned Boerlage Brent 1994 Link Strength in Bayesian Networks Tech Report 94 17 Dept Computer Science Univ of British Columbia BC Charniak Eugene 1991 Bayesian networks without tears in AZ Magazine Winter 1991 12 4 50 63 Dean Thomas L and Michael P Wellman 1991 Planning and Control Morgan Kaufmann San Mateo CA Heckerman David 1993 Causal independence for knowledge acquisition and inference in Uncertainty in Artificial Intelligence Proc of the Ninth Conf July Washington DC David Heckerman and Abe Mamdani eds Morgan Kaufmann San Mateo Heckerman David and Jack Breese 1994 A new look at causal independence in Uncertainty in Artificial Intelligence Proc of the Tenth Conf July Seattle WA Ramon Lopez de Mantaras and David Poole eds Morgan Ka
2. 11 5 Copying and Pasting Graphics After cutting or copying all or part of a network you can paste the graphics into other Windows applications such as Microsoft Word PowerPoint Works etc If some nodes are selected when the Copy command is done then graphics for only those nodes will be placed in the clipboard If no nodes are selected then graphics for the whole network will be The nodes will be drawn with the same design style and font as they are shown on the screen so you may want to adjust this with the Style menu before copying to the clipboard 80 To see what is currently in the clipboard you may find it useful to use the Clipboard Viewer program which is supplied with MS Windows On a normal installation it can be found at Start Programs gt Accessories gt Clipboard Viewer After you paste the graphic into another program you may want to adjust its size and shape so that the aspect ratio i e height width ratio is similar to the belief network it came from in order to achieve the best appearance If the aspect ratio is very different from the original some of the characters may overlap Netica graphics are pasted into other programs as enhanced metafiles When pasting into Word 97 it is often more convenient to have the graphic as a Word 97 picture You can achieve this by first pasting it into Word then while it is still selected do a Cut then do an Edit Paste Special and choose Pict
3. 4 10 4 Link Delay ees iiie eden leen exo reas RI Eo eats 4 10 5 INOUE States eerte dl end ee tette tiet piae qos 4 10 6 Node Ranges enint rer kansiin de ponga ced 4 10 7 When Changed e aerae eere erae Ua pesa Poe ese 5 Node Relationships 5 1 Obtaining a Relation Dialog Box eee 5 2 Meaning of the Tables ose ien lr dees suaead a as 5 3 Changing Table Bntfies uoi oec otro I RUP sn 5 4 Buttons in the Relation Dialog Box eese 5 5 Deterministic Chance Pop Up ii e eee oret teo nre REP esters eve 5 6 Serolling and RestZHig o ansa e et reet ON EH INS RUE dash Eben gEE 5 7 Unspecified and Impossible Cell Values esses 5 8 Selecting Cutting and Pasting xs ice dant ded de be rm saan 5 9 Relation Menu Commands esee 5 10 Multiple Dialogs for One Node eee 6 Decision Problems 6 1 Constructing a Decision Network eere 6 2 No Forgetting Links isi Lor eh nasi ee toe eU ERR E Y Dade 6 3 Solving a Decision Network 0 cecccecsscceeeseceesteceeseeeseeesseeeeaees GAL NIodeLlteratio auod oor eee orto t pee o pa ose Epia 6 5 What if Decision Analysis esee nennen 7 Network Libraries 7 1 Disconnecting and Reconnecting Links ees 7 2 Making and Using Network Libraries eeees 8 Transforming a Network Gol Link Reversal
4. but does not care about how nodes are linked together In that case you may also want to hide some of the nodes which are of no interest to the end user To avoid confusion it is not possible to display some links and hide others When the links are hidden Style gt Net Hide Links will be check marked and choosing it from the menu again will redisplay the links The remaining 3 choices of the Style Net submenu are for those who are familiar with the process of belief network compiling and wish to see how it is being done They allow you to switch between showing the link structure of the network which was originally constructed Style Net Regular Dag the link structure of the Markov network which can be derived from it Style Net Markov Net and the link structure of the triangulated graph derived from the Markov network Style gt Net Triangulated The triangulated graph is used internally to determine the cliques when compiling the network and a number is displayed with each node to indicate its position in the elimination order of the compilation The Triangulated and Markov Net styles are only for viewing the network printing it changing styles and copying its graphics with no nodes selected If you try to do any other operation the style will automatically change back to Regular Dag Before you select these from the menu you may want to save your network since they will loose information about link bends
5. but possibly many more if they don t take up much memory If you are undoing operations and the Edit Undo menu item turns dim it means you have undone all the operations that Netica has remembered which may only be a couple if you have only done a couple since the last file save If you are redoing operations and the Edit Redo menu item turns dim it means that you have restored all the operations that were previously undone The operations done in each window are remembered separately so if you return to window A after working in another window for a while you can still undo operations previously done in window A 3 5 Selecting Nodes and Links Many operations on nodes are done by first selecting one or more nodes and then choosing the operation to do Netica indicates a selected node by drawing it with inverted colors You can select a node by clicking once on it To select a group of nodes you can click down on the background and then drag the selection rectangle to include at least a part of each of them To unselect all the nodes currently selected just click once on the background within the window To select all the nodes in the network you can use the Edit Select All command or press Ctrl A When you select new nodes any nodes that were previously selected will become unselected unless you hold down the shift key while clicking or dragging In that case the selected status of the new node s will be reversed al
6. there with the cursor returning to normal Instead of the tool button you can use the appropriate command from the Modify menu or its shortcut key equivalent F9 F11 To add a series of nodes double click on the button for the type of nodes you wish to add or double press one of the keys F9 F11 i e press it twice in quick succession The cursor will change to the shape of the node as before but now it will be darkened indicating that a number of nodes may be added without pressing the node button each time To exit this node adding mode click again on the node adding button or press the node adding Fx key again or click on the pointer button or click on a different node adding button or press a different node adding key When a node is first added it will be selected i e drawn with inverted color Whenever a node is selected you can press the Enter key to bring up a dialog box for setting node characteristics and when the dialog box first comes up its field for setting the node s name is selected for changing This makes it possible to quickly add a node with a certain name Just click the appropriately shaped cursor where you want the node to be press the Enter key type the name and then press the Enter key again There is no need to think about the dialog box or wait for it to be fully drawn Using the dialog box to change other node characteristics is described in chapter 4 3 3 Adding Links To add a link fr
7. If you double click on the Position node you can see the equation which defines the new position in terms of the old position and the velocity It involves the constant dt whose value may be changed by right clicking on the dt node to provide a different amount of time between time slices By clicking down on the selector that originally says Equation you can choose Ranges to see how the node has been discretized Later you can edit this list to change the discretization by changing the numbers or adding new numbers The first step is to generate probability tables for the current discretization Select the Position and Velocity nodes and do a Relation Equation to Table menu command Enter 100 when prompted for the number of samples per cell Then do a Relation Harden menu command and press Enter to accept the default value for hardening Next you generate a time expanded version of the network by doing a Network Expand Time menu command you can enter 7 when it asks you for the total time This will make a new window with a new network in it You will probably want to make this window wider in the usual way by resizing it The new network is a regular belief network with each Position and 15 Velocity node representing the position and velocity at a new point in time with nodes to the right corresponding to later times There are 3 disconnected links on the two first nodes We have no initial knowledge of the pos
8. The title of the window will be set when you do a File gt Save or a File Save As command You will often find it easier to build a network by modifying an existing one To do so read in the existing one with File gt Open save it under the name of the new network with File Save As and then make the desired modifications occasionally saving it with File Save You can open as many network windows as you wish As with any Windows application the current operation always applies to the active window which is the one in front with the non dim title bar You can make a window active by clicking on an exposed part of it or by choosing its title from the Window menu When you are done with a window you can close it by clicking in the X box at its upper right or by making sure it is the active window and then doing a File Close command if you have made unsaved changes Netica will ask if you want to save them before closing the window 3 2 Adding Nodes The tool bar buttons with the gray oval blue rectangle and green hexagon are used for adding nature nodes i e chance or deterministic nodes decision nodes or utility nodes also known as value nodes respectively When you click on the appropriate button and then move the cursor over the active window it will change to the shape of the node to be added Next click Eq on the place in the network window where you want the node to appear and it will be added
9. Updating from the menu When auto updating is off and you wish to do belief updating use the Network Update command or click on the right arrow tool bar button they will be dimmed if belief updating is not currently required for the network or if it is not compiled If auto updating is turned off and you enter a new finding or if no findings are entered but belief updating was never done then the belief bars or belief meters will not display valid results and so they are drawn fuzzy dotted rather than in solid black The reason they are not removed completely is that you may want to see what the beliefs were at the point of the last belief updating 2 7 Negative and Likelihood Findings In the sections above we saw how to enter positive findings into a belief network to do probabilistic inference 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 s23 finding that the temperature is not medium
10. and 4 If the case is not already in the belief network you enter it into the network as findings see chapter 2 Only positive findings will be used negative and likelihood findings will be ignored Then you select the nodes whose probabilities you would like to have revised to account for the case if possible Usually you would like all possible nodes to have their probabilities revised so you would select all the nodes or don t select any nodes which is equivalent Then click on the tool bar button having an arrow pointing from the yellow case symbol to the green relation symbol inverted V s or do a Relation Incorporate Case menu command You will be queried for a degree which is normally 1 By making it 2 you can achieve the same effect as learning the same case twice and equivalently for other numbers By making it 1 you can exactly unlearn a case that was earlier learned with degree 1 and so on for other negative numbers Don t try to unlearn cases that were never learned or to unlearn them with greater degree than they were learned During the learning selected nodes for which the case provides sufficient data will have their probabilities revised a small amount to account for the case and their appropriate experience levels increased slightly as described in section 10 2 below gus 10 1 2 Learning From a Case File The batch mode way of revising probabilities does exactly the same thing as the one by one
11. be added from the parents of the parent node to the child node and from the parents of the child node to the parent node which will increase the complexity of 60 the network Technically speaking all links added will be confined to the parent node and its Markov boundary When links are added the size of conditional probability tables may grow significantly and sometimes enormously The size of the tables is the product of the number of states of all the parents so the size of the tables can grow exponentially When link reversals result in a node having many parents the operation may be slow or Netica may report that there is not enough memory available Occasionally during a reversal links from the parents of the parent node to the child node and from the parents of the child node to the parent node will disappear resulting in a simpler network For example reversing the link from P to C might result in additional links going into P and C but when the link is reversed again so that it has its original orientation those links will disappear resulting in the original network providing all the nodes have nondegenerate probability tables and that rounding inaccuracies are small Often a network which is simpler due to the direction of its links provides a better model of the world For example it usually represents true causality more accurately it may be better at generalizing and of course it allows for faster computation S
12. changes the multiple 100 bars of other nodes By trying each of the possibilities you can map out all the configurations that are at the highest probability level You must be careful using the MPE Generally it is not as good as posterior probability i e regular updating for decision problems or providing prediction or diagnosis probabilities Its results can change with the introduction of irrelevant variables And it can be deceptive when even the most probable explanation is extremely unlikely What the MPE is useful for is explaining and aiding understanding If an agent finds the results of regular belief updating questionable and asks you to provide a scenario for which the beliefs are upheld you can use the MPE to find that scenario People sometimes find a completely specified scenario easier to understand And sometimes you can gain insights by putting the belief network in MPE mode entering the evidence observing the most probable configuration and then experimenting with adding extra evidence to explore a set of probable configurations close to the most probable one while seeing how changing one node effects the others 26 3 Constructing Belief and Decision Networks 3 1 Opening a Window The first step in creating a new network is to open a window for it Use File New Network or click on the tool bar button with the three connected nodes and the golden glint A window will appear in which you can build the network
13. command All the nodes of the network will be used to generate the cases but columns will only be made for the selected ones You will be queried for how many cases to generate the file name for the case file where to put it and how much missing data you want Normally you will enter 0 for the amount of missing data but if you want to have a case file with asterisks for some fraction of the fields enter that fraction e g entering 0 25 means 25 of the values will be missing As an example if you do a Network gt Generate Cases command with Asia dne from the Examples folder and enter 120 asia cases and 0 to the query dialogs then you will obtain a case file similar to that shown in the preceding section 69 10 Learning from Cases Belief network learning is the automatic process of determining a suitable belief network given data in the form of cases Each case 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 describe the event object etc as described in the last chapter Each variable becomes a node in the learned network unless you want to ignore some of them and the various values it takes on become that node s states Some cases may not have values for some variables that other cases do which is known as missing data The learned network can be used to analyze a new case drawn from the same
14. degree of learning 71 delay of link 40 Delete button in node dialog box 38 delete key 32 deleting links 32 deleting nodes 32 deleting states of a node 38 Dempster Shafer 72 description of Netica 7 description text of node 39 Determin Chance selector of relation dialog box 46 deterministic 18 deterministic node 37 deterministic vs probabilistic node changing 46 diagnosis 70 Dirichilet distribution 75 disclaimer 2 8 disconnecting links 32 57 discrete vs continuous 36 discretizing 37 38 41 66 display style 77 DNET 1 file format 31 double press 28 dragging 11 Drawing Balls example 72 drawing size 34 duplicating nodes 33 Edit Copy menu command 33 48 58 80 86 Edit Cut menu command 33 Edit Delete menu command 32 Edit Duplicate menu command 33 Edit Paste menu command 33 48 58 Edit Redo menu command 29 Edit Select All menu command 29 Edit Undo menu command 29 45 elimination order 80 empty cells in relation dialog box 47 end key 34 46 enhanced metafile 81 enter key 28 35 entering findings 22 equation of node 40 equations for node relations 82 equivalent sample size 73 ess 73 evidence 19 22 evidence node 62 examples Asia medical 20 69 diagram 21 Car Buyer 54 Drawing Balls 72 Flow Instrument 56 58 Political Riding 66 reducing large net 62 relation dialog box 44 Umbrella 52 Weather 56 Examples folder 8 exiting Netica 9 expected v
15. dialog boxes it must be the active window which means it is in front with its title bar non dim To make a relation dialog box the active window just click on an exposed part of it or choose its name from the Windows menu 5 2 Meaning of the Tables For a belief or decision network to be fully specified there must be a relation stored at each nature or utility node which expresses the value of that node in terms of its parents or as a constant if the node has no parents If the node is deterministic then the relation will be a function which provides a value for the child for each possible configuration of parent values If the node is probabilistic i e a chance node then the relation must provide a probability for each state of the child for each possible configuration of parent values As For example suppose node A which can take on values Low Medium or High and node B which can take on values True or False are the two parents of node C which can take on values Small Midsize or Large It is best to think of the relation between them as being located at node C the child and its relation dialog box might look something like this Node M Chance Mi Small Midsize Large True 10 000 35 000 55 000 False 17 250 82 750 0 000 Medium True 12 100 Medium False 33 333 33 333 33 333 High True x x x High False 54 328 45 672 3 2e 012 HZ On the left hand side is a vertical list of all the configuration
16. 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 If the values of some of the variables are unknown for some of the cases then an asterisk is put in the file instead of the value this is known as missing data A single case file is the same as one with multiple cases except it just has 1 case There may be as many spaces or tabs at the end of a line as desired and there may also be C or C style comments i e a double slash followed by any text 67 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 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 As an example of a case file here is a listing of asia cases which is produced by the example in the section below the case file you obtain may be a little different since random numbers ar
17. folder and you may place it wherever you want on your hard disk and move it at any time You should look at README txt to see if it contains any special instructions or warnings Within this folder is a file called Netica or Netica exe with a large square blue icon It is the file you double click to run Netica You can try running it and doing the operations described in Quick Tour below to verify that everything is installed and working properly The first time you run it you will be requested to enter a password Your password is written on the invoice which is mailed to you and is also sent to you by email if you ordered it over the Internet If you have two or more different versions of Netica installed at the same time the default version the one that runs when you double click a document icon will be the one that was run last To completely remove Netica from your hard disk simply drag the folder containing Netica into the recycle bin Netica does not add any files to any other folders except of course your document dne files get placed where you request 1 3 Menu Commands and Tool Bar In this manual menu items are indicated in bold with arrows indicating choices or submenus so File Open means choose Open from the File menu Most menu items have a corresponding tool bar button and you can discover what the buttons do by resting the cursor on them briefly Some of the tool bar buttons discussed in this manual may no
18. from a previous solution of a decision network select the decision node and change it into a nature node by clicking on the gray ellipse toolbar button while holding down the Ctrl gt key Then solve the network in the usual way and observe the changes to the other decision functions and the change to the maximum expected utility Of course you can use undo to return to the original situation In general when you want to fix a decision node to a certain decision function while you continue your analysis you temporarily change it into a nature node 55 7 Network 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 networks to be used in different situations That relation may have been learned from data or entered by an expert Each new network 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 network consisting of a node called Weather connected to a node called Forecast You could put the link between them either way since in this situation you can t really capture causation they are both caused by other variables such as the weather at earlier times but say you put the link from weather to forecast because often its better to put li
19. hand side of the table contains a vertical list of parent configurations and for each configuration the right hand side has a few probabilities expressed as percentages Each column of the right hand side corresponds to a different state of the node So each number represents the conditional probability that the node takes on the state indicated by the column the number is in given that the parents have the configuration indicated by the row the number is in If the node is deterministic e g the TbOrCa node then the relation dialog box will display a function table This is the same as the conditional probability table except that the right hand side simply has the state of the node which is the function value for that parent configuration To work with an example of a more complex belief network also in the medical domain open the file called Alarm You can compile it and do inference in the same way as you did with Asia If you have entered a number of findings for a particular case and wish to save them in their own file do a File Save Case As command and enter the file name in the dialog box which appears If you want to work on a new case do Network Remove Findings and then enter the new findings To recover the original case do File gt Get Case and choose its name from the dialog box which appears When you are done with a network window you can get rid of it by clicking in its X box at the upper right or by makin
20. node Our goal is to find a decision function which will maximize the expected value of the utility node This is accomplished by doing Network Optimize Decisions After doing this command when you look at the relation dialog for the decision node it will display the discovered decision function you will have to click the Load button if you didn t freshly open the dialog Absorbing all the nodes and then opening the relation dialog for the utility node will show the expected utility You can then use an Undo command to return the network to its original state If you want to try another influence diagram open Car_Buyer_Neapolitan which is described in Neapolitan90 and is based on the classic Car Buyer influence diagram It involves two sequential decisions about whether to do some tests and then whether to buy a certain used car The optimal decisions turn out to be not to do any tests D none but to buy the car B Buy when D none 1 4 5 Equations and Time Expansions Open the belief network called Bouncing It is designed to model a ball which bounces back and forth in a straight line between two parallel barriers without loosing any energy at each bounce Initially we have no knowledge of the position or velocity of the ball The Position and Velocity nodes stand for the position and velocity at each instance of time and are connected together with brown time delay links as well as a regular black link
21. node was last changed based on the clock in your computer This value is similar to the one maintained by your computer operating system for when each file was last changed but it can be more useful for belief networks since it actually records the time of change not just the time of file saving and it provides a separate value for each node You cannot change this value it is for observation only If no value appears it means that the time of the last change was not saved in the belief network file and the node hasn t been changed since reading from file 42 5 Node Relationships In the previous two chapters we saw how to create nodes set their characteristics such as name or number of states and link them together This chapter will explain how to enter the actual relationships nodes have with each other which are most often in the form of conditional probability tables We enter change or view the relationship using a relation dialog box 5 1 Obtaining a Relation Dialog Box The way to obtain the relation dialog box for a node is to select it and then click the tool button with the green relation tree looks like two inverted V s or do a Relation gt View Edit menu command You may have several relation dialog boxes on the screen at the same time and you may alternate between using different relation dialog boxes different node dialog boxes and directly working in the network window To use one of the relation
22. nodes going to a node not being cut or copied will not be copied Networks may be copied and pasted into other programs such as Microsoft Word See section 11 5 Copying and Pasting Graphics for more information on this Nodes may be duplicated within their network by selecting them and doing an Edit Duplicate menu command All links between them and all their characteristics and probability tables will be duplicated as in the copy paste situation but any links to them from parent nodes not being duplicated are handled differently Instead of being disconnected they are duplicated as well which is especially useful to create nodes representing repeated independent imperfect Observations of some node i e virtual evidence Since every node name in a network must be unique a node s name must be changed when duplicating it into a network already having that name This is done by adding a number to the uds end of the old name or incrementing the number if there already is one Of course node titles don t have to be unique so after duplicating or pasting you may have several nodes with the same title 3 12 Drawing Size and Scrolling Using the scroll bars you can move around to view or work on various areas of the network The lt home gt lt end gt lt page up gt and lt page down gt keys may be used as well While you are moving a node or a link bend you can make the window scroll by attempting to drag them outside th
23. one motion by first selecting the link and then dragging the hilited box at the link tail from the old parent to the new When reconnecting a link the new parent must be compatible with the old one in certain ways For example since the conditional probability table is maintained during the reconnection the new parent must have the same number of states as the old If there is any incompatibility between parents an error message will be displayed 3 11 Cut Copy Paste and Duplicate Nodes Selected nodes can be removed from the network and transferred to the clipboard with an Edit Cut command from the menu or pressing Ctrl X keys Alternately they can be entered into the clipboard without removing them from the network using an Edit Copy menu command or pressing Ctrl C keys If no nodes are selected when the cut or copy command is done the whole network will be cut or copied to the clipboard Once the nodes are in the clipboard you can duplicate them into any network by opening the window for that network optionally clicking in it where you want them to be placed and then doing an Edit Paste menu command or pressing Ctrl V keys All links between the transferred nodes all their characteristics and all their conditional probability tables will maintained during the transfers Links that enter cut or copied nodes from a node not being cut or copied will appear as disconnected links in the duplicate Links that exit cut or copied
24. other mathematical functions Has facilities for the easy discretization of continuous variables t is possible to represent networks with nodes whose values change over time a persistence is defined for such nodes and to have links with time delays which allows cycles The software can automatically convert these networks into expanded regular networks covering a limited period of time e Supports documentation and tracking of every node and network with comments titles author when last changed locking etc Has no built in limits on the size or complexity of networks so they are limited only by available memory Can work hand in hand with the Netica API Programmer s Library for example sharing the same files 1 2 Installation Before installing or using Netica be sure that you accept the License Agreement which is provided with the software on a separate document Netica requires a PC with an 80386 or later processor running Microsoft Windows 95 or Windows NT 4 0 Netica can be installed to consume less than 2 MB of hard disk space To install Netica the first step is to get NeticaZip exe on your hard disk If Netica was mailed to you copy it from the supplied floppy disk otherwise download it from www norsys com When you double click it a folder called Netica will be created containing Netica exe the license agreement README txt and a folder of example files All the files required for Netica are in this
25. parent configurations may become possible You can set a chance cell to x by selecting the cell and then typing x and a deterministic cell to x by choosing Impossible from the cell s pop up menu For chance nodes if one cell has an x then all the cells in that row must have an x because they all correspond to the same parent configuration 47 5 8 Selecting Cutting and Pasting To do operations on a restricted group of cells you first select them which turns their background to the hilite color To select cells of a probabilistic relation you click down in one cell and drag the mouse to another cell before releasing the mouse button While you are moving the mouse all the cells in the rectangle between the original cell and the current mouse position will be hilited The cell you first click down in must not be the cell you are currently editing i e the only selected cell or the cell with the insertion point blinking in it or Netica will think that you are doing an operation to edit just that cell If you wish the selected area to extend beyond the window boundary just drag outside the boundary and the window will automatically scroll Once you have made a selection you can hold down the shift key while you click on another cell to extend or reduce the selection To select cells of a deterministic relation you click down on the area slightly to the left of the cell if you click right on the cell instead of selecting you
26. starts off in a state of ignorance All probabilities start as uniform and experience starts off as 1 For each case to be learned the following is done Only nodes for which the case supplies a value finding and supplies values for all of its parents have their experience and conditional probabilities 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 set by you just before learning begins 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 prob as follows prob probe exper degree exper The other probabilities in that vector are changed by probi prob exper exper which will keep the vector normalized exper and exper act as the old and new normalization constants 10 3 Bayesian Learning If you are not interested in a technical discussion of how Netica s learning is a form of Bayesian learning you should skip this section Generally speaking it is a wise idea to r
27. tE 27 3 S Adding LINKS r ira e e aa cade M e e a Eo Em uet 28 3 4 Undoing and Redot g aporte abet da oce adnata 29 2 Selecting Nodesand LINKS sristi oat eee ote doa a 29 3 6 Moving Nodes and AutoGrid eene 30 3 7 Reshaping Link ais coii eer dcc ra a Sepe ES 30 3 8 Saving a Network to a PIIe uid occhi rep edu teens 31 3 9 Deleting Nodes and D3nks ii eub Cro eon ort ot eat 32 3 10 Disconnecting and Reconnecting Links ues 32 3 11 Cut Copy Paste and Duplicate Nodes esses 33 3 12 Drawing Size and Scrolling na ederet a reene 34 4 Changing Node Characteristics 35 4 1 Obtaining the Node Dialog Box eee 35 AD Makina C albe spese Toce Sees Reeve ette en te e a e goa 35 4 3 NDde NaMe uio cea ran eget ve sa ideo Egan toa Pa oe Uo Ese e eau de o bed apu RU AA NGG Title em T R E T E 4 5 Node is Discrete or Continuous ccceceesseceeeessececeeseeceeeeeeaaeeeenees 6 Node ASAIN EEEE EEE teres dit E E 4 7 Node OUS queden eebg reali pela cepe a a Ei 4 8 Node State Ralbse i oe iedives dee peciit test eee a Uto den ge da e Ie epa oia Z9 Node Side alie scissors a o Baadshah nll ad o hein dee 4 10 Multi Purpose BOX eic iet suavesantasvsnsetods eee 4 10 1 Node Deseription eer eerte ee tete enne tenga ege esa 4 10 2 Node Equation 5 ine iere nis 4 10 3 Input Name eee eet etae sut es Pega eeu tae e un pesa iube eda
28. the one by one method described in the preceding section for each of the cases in the file The degree that you supply will be applied to each case of the file in the same way as described in the preceding section except if the case file has a NumCases column see section 9 2 then the degree will first be multiplied by the multiplicity from that column As Netica processes the cases it reports its progress in the Messages window 10 2 Experience There has been considerable controversy over the best way to represent uncertainty with some of the suggestions being probability fuzzy logic nonmonotonic logic belief functions Dempster Shafer etc Currently probability and fuzzy logic are the most practical methods for most applications 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 only 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 bag If you had 72 to supply a probability that you were going to draw a white ball it should 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 th
29. 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 likelihood finding also known as virtual evidence 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 we 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 actual 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 You can enter a negative finding for a belief bar node of a compiled network by holding down the shift key while you click on the name of the finding you know its not You can enter a likelihood finding for a no
30. to recompile between each switch as is indicated by all the belief bars turning gray You then enter findings in the usual way and it does MPE updating immediately afterwards if Network Automatic Updating is on or otherwise just after a Network Update command After updating each node will have a belief bar at the 10096 level and usually some bars at lower levels You can read off the most probable configuration by taking for each node the state with the bar at the 100 level The shorter bars indicate the relative probabilities of the other states given that the other nodes are in the most probable configuration scaled by the same factor used to bring the longest bar to 100 Of course the bars don t add to 100 so if you are ever using Netica and are confused that every node has a 100 bar and there are also some other nonzero bars it is because MPE updating is on To avoid the possibility of accidentally doing MPE updating when regular updating is expected all networks start with the MPE feature turned off even if MPE was on when the network was last saved Sometimes two or more states of the same node have bars that are at the 100 level This indicates that there is more than one configuration with the highest probability i e the 28 configurations have the same probability If more than one node has this then you should choose one of the states and enter artificial evidence that the node is in that state to see how it
31. way but for a whole file of cases at once See chapter 9 Cases and Case Files for information on creating a file of cases Before learning begins you must have a belief network constructed whose nodes are the variables i e attributes of the cases It is okay if it has additional nodes related or unrelated to the cases in the file If you don t already have a network constructed or the network you have doesn t include all the variables in the case file that you wish you can use the Modify gt Add Case File Nodes menu command It will scan through a case file and add to the current network new nodes for any variables that it discovers in the case file that aren t already in the network The states of the new nodes will be all the possible values discovered from the case file If your network already has a node with the same name as some variable from the case file but that node doesn t have all the states that are mentioned in the case file for that variable then those states will be added to the node unless the node has a state called other After Netica has added all the nodes you move them to the positions you want delete any that you aren t interested in and then add links between them and to or from any other nodes in the network to capture the dependencies that you wish When you do a Relation gt Incorp Case File menu command Netica will ask you for a case file and a degree It will then do the same thing as
32. you want to change a few digits Remember to enter the number as a percentage If you want to enter probabilities as decimal fractions e g 0 25 rather than percentages e g 25 see the normalize command in section 5 9 below If a cell is being edited the insertion point will be flashing where new digits will enter You can use the left or right arrow keys to move it around within the number and if it gets to the edge of the number it will jump to the next cell in that direction Further presses will jump to subsequent cells in that direction and the up and down arrow keys can be used in the same way to jump to cells above or below the currently selected or edited cell Pressing the tab key jumps to the next cell which is the cell to the right of the current one unless it is at the end of the line in which case it is the first cell on the next line 5 4 Buttons in the Relation Dialog Box Whenever you make any changes within the relation dialog box they don t actually affect the node until you click on the Apply or Okay buttons Then all the settings are transferred to the node in the network The only difference between the Apply and Okay buttons is that the Okay button removes the dialog after transferring the settings while the Apply button doesn t Clicking on the Load button will transfer all the values from the node in the network to the dialog box There are two main uses for this button The first is if you make a mistak
33. 1 2 83 158 Zhang Lianwen Nevin and David Poole 1996 Exploiting causal independence in Bayesian network inference in Journal of Artificial Intelligence Research 5 301 328 84 14 Index 67 absorb node tool 62 absorbing a node 62 active window 21 add link tool 28 Add No Forgetting Links menu command 53 added links during reversal 60 adding links 28 adding nodes 27 adding states to node 38 address of Norsys 2 agents 17 AL 17 algorithms used by Netica decision problems 64 node absorption 64 probabilistic inference 16 17 Alt PrintScreen 81 application areas 6 Apply button in node dialog box 35 in relation dialog box 45 arrow keys 30 31 in relation dialog box 45 artificial intelligence 17 Asia medical example 20 69 diagram 21 asia cases 68 60 aspect ratio 81 asterisk 67 attribute value 67 autogrid 30 31 auto updating 23 24 batch mode learning 72 Bayesian network 18 beep sound 9 belief 19 belief functions 72 belief network 18 adaptive 75 compiling 21 file format 31 learning 70 new 27 belief network libraries 56 belief updating 19 85 manual 23 slow 23 belief bars automatically changing to 21 fuzzy 23 picture 21 Belief Bars node style 78 belief meter fuzzy 23 Belief Meter node style 79 bends in links 30 beta functions 75 bibliography 83 bitmap program 81 blank cells in relation dialog box 47 Boerlage94 61 83 border of n
34. 27 Modify Add Case File Nodes menu command 72 Modify Add Link menu command 28 Modify Disconnect Links menu command 32 57 most probable explanation 25 moving nodes 30 MPE 25 MSPaint pasting to 81 multi case files 66 multi line title 36 multiple agents 53 multiple node dialog boxes 50 multiple relation dialog boxes 50 multiplicity of cases 68 multi purpose box 39 multi purpose selector 39 Name edit box of node dialog box 36 name of node 36 77 name of node changing automatically 34 nature node 37 51 Nature Dec selector of node dialog box 37 Neapolitan90 17 83 negative finding 23 Netica API 6 59 67 Netica Application 6 Netica description 7 Netica Messages window 9 Netica Programmer s Library 6 59 67 NeticaZip exe 8 network libraries 56 network reduction 62 network transforms 60 Network Absorb Nodes menu command 62 Network Add No Forgetting Links menu command 53 Network Automatic Updating menu command 23 Network Compile menu command 21 Network Generate menu command 69 N N N N etwork Most Probable Expl menu command 25 etwork Optimize Decisions menu command 53 etwork Remove Findings menu command 22 66 etwork Update menu command 23 New button in node dialog box 38 node 18 adding 27 72 adding states 38 72 changing 35 copying 33 cutting 33 darkening 22 deleting 32 description text 39 discrete vs continuous 36 dupli
35. 38 To set or change the range of the current state simply type a number in the appropriate box States are arranged in a contiguous and increasing or decreasing monotonic way which means that the upper end of one state range will always be the lower end of range of the neighboring state As you type one of these in Netica will fill in the other as well so that when you change the current state you will see the number you just entered in one of the Range boxes It is okay if the lower and upper bounds of the range are the same The numbers you enter may be integers decimal numbers scientific notation numbers infinity or infinity 4 9 Node State Value If a node dialog box is for a discrete node then immediately below the state name edit box will be a box labeled Value This is to associate a real number value with each state You will rarely need this but occasionally it is useful For example in a bang bang control system state 0 Off may map to 0 2 volts and state 1 On may map to 6 0 volts If this node is the parent of a node with an equation then the real values will be supplied to the equation see chapter 12 Equations for more information To set or change the real number associated with the current state simply type a number in the box See section 4 7 above on how to change the current state You may find it easier to use the Multi Purpose Box described in section 4 10 6 below to enter or c
36. Files The case files described above consisted of a single case but it is possible to store many cases in one case file These case files act as databases they may be used to swap cases in and out of a network as additional findings are obtained or beliefs required to transfer a case from one network to another or as data to learn a new network There are several different ways you can make a file of cases One possibility is to use a text editor or a word processing program and manually construct it according to the specification in the section below be sure to save it as a Text Only file if you use a word processing program If the data is in a spreadsheet program usually you can just copy the data from the spreadsheet to 66 the clipboard and then paste it into the text editor window and it will come out in the required format You will have to add the two header lines described in the section below If you wish to create a multi case file consisting of random cases sampled from a particular distribution Netica can make it as described in section 9 3 Generating Random Cases below Another way to create a multi case file is to write a computer program that creates it Using the Netica API Programmer s Library may be especially useful for this purpose since it can create such a file with just a few function calls It can also be used to update and otherwise maintain case files and to read them and do belief network learni
37. Netica Application for Belief Networks and Influence Diagrams User s Guide Version 1 05 for Windows Netica Application User s Guide Version 1 05 March 15 1997 Copyright 1996 1997 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 2315 Dunbar Street Vancouver BC Canada V6R 3N1 WWW norsys com Netica and Norsys are trademarks of Norsys Software Corp Microsoft MS DOS Windows and Windows NT are registered trademarks of Microsoft Inc Macintosh is a trademark licensed to Apple Computer Inc Balloon Help is a trademark of and Apple is a registered trademark of Apple Computer Inc UNIX is a registered trademark of AT amp T IBM OS 2 and Presentation Manager are registered trademarks and PowerPC is a trademark of International Business Machines Unicode is a trademark of Unicode Inc PostScript is a registered trademark of Adobe Systems Inc Intel is a registered trademark and Pentium is a trademark of Intel Corporation Other brands and product names are trademarks of their respective holders While every precaution has been taken in the preparation of this document we assume no responsibility for errors or omissions Neither is any liability assumed for damages resulting from the use of the information contained herein Contents 1 Getti
38. Of course the network is destroyed in the process but you can recover it by doing an Edit Undo command Normally it is better to do inference by compiling the network and doing belief updating as described in 535 chapter 2 Probabilistic Inference but sometimes additional insights are gained by using node absorption for inference It should be mentioned that node absorption will also work with decision networks see chapter 6 Decision Problems to find optimal decisions To solve a decision network select all its nodes and then do a node absorption command click on the star tool button The nature nodes will all be absorbed out When a decision node is absorbed it is not removed from the network instead it is completely disconnected and its decision table set to the optimal decision function Utility nodes are also left so you can see the expected utility The algorithm used is described in Shachter86 Shachter88 and Shachter89 When using node absorption to solve decision problems the decision nodes must have no forgetting links which are described in section 6 1 Also there must be only one utility node with no descendants and if the nodes to absorb do not include all the nodes in the network they must consist of a descendant subnetwork So if nodes are absorbed one by one a suitable order must be used These restrictions are explained in more detail in the Shachter references mentioned above If any of these restriction
39. The previous paragraph stated that when solving a decision network we find values for each of the decision nodes But if there are some links entering a decision node we actually find a decision value for each possible configuration of values of the parents This is a contingent plan with a form like if I observe A high and B no then I will do X if I observe A low and B yes then I will do Y and so on So solving a network finds a decision function for each decision node i e a function which gives a decision value for each possible set of parent values If there are a number of decision nodes possibly corresponding to decisions made at different points in time then solving the network will find a decision function for each of them and this set of decision functions is known as a policy Itisa 5 full conditional plan specifying what to do in each possible contingency based on the information that will be available As an example let s consider a very tiny decision network from Ross Shachter known as Umbrella located in the Examples folder It has 2 nature nodes representing the weather forecast in the morning sunny cloudy or rainy and whether or not it actually rains during the day rain or no_rain It has a decision node of whether or not to take an umbrella and a utility node that measures the decision maker s level of satisfaction There is a link from Weather to Forecast capturing the believed correlation betwe
40. When it is finished if you examine a few nodes with the node relation dialog you will see the learned probability distributions You can compile the network and do inference paste parts of it into a decision network absorb nodes etc Netica can also be used to generate files of cases which follow the probability distribution of a belief network i e sample from the belief network These cases can be used as realistic examples of possible scenarios or as synthetic data for learning experiments Simply select those nodes of the network for which you want columns in the case file and then do Network Generate Cases You will be queried for the number of cases to generate the name of the file to create and how much missing data you want enter 0 for none 1 for all missing 1 4 4 Decision Problems Use File Open to read the decision network also known as an influence diagram called Umbrella By opening relation dialogs for the nature nodes yellow ovals also known as chance nodes you can observe their conditional probability relations as described in the first section of this Quick Tour By opening a relation dialog for the utility node green hexagon also known as a value node you can see its utility function If you look at the relation dialog for the 4 decision node blue rectangle you will see that the node does not yet have any functional relation which indicates that there is no decision function associated with the
41. When the node dialog box first appears the existing name of the node is selected so if you just type a new name it will replace the existing name When you enter a new node name Netica will check that it meets the restrictions of an Dname It must start with a simple letter a z or A Z it must be composed only of simple letters digits and underscores _ and it must be 30 or fewer characters long Also it must be different from the names of all other nodes in the network If you want to circumvent any of these restrictions you can also give the node a title which has no such restrictions 4 4 Node Title The node dialog box has a text edit box labeled Title so that you can give the node a title which will be used to label the node on network diagrams There are no restrictions on what you may put in a title and by using the Enter key you can make the title more than one line long By putting a blank line at the beginning or end of the title or putting a space character at the beginning or end of a title line you can effectively add some space between the outside border of a node and the writing within If the title is longer or taller than the text entry box you can scroll it using the arrow keys The title is only used to label the node anything more detailed should go in the description of the node Keep in mind that some unusual characters may display differently when the font is changed or if the network is displayed on anot
42. ach time To select a node or link click once on it with the regular pointer cursor and it will become hilited A group of nodes may be selected by clicking down on the background within the window and then moving the mouse with the button depressed i e dragging so that the selection rectangle is over them You can add to or remove from a group of selected nodes by holding down the shift key while you select the new nodes To delete nodes or links select them and then press the delete key After doing any operation you can undo it with Edit gt Undo or pressing Ctrl Z and by repeating this you can undo operations previous to that one at least 4 operations and sometimes more if they don t take much memory After undoing one or more operations you can redo them one by one with Edit Redo or pressing Ctrl Shift Z When exploring with Netica it is very useful to be able to try a few operations and then easily undo them A node can be moved by clicking down on it dragging it to its new position and then releasing the mouse button To move a group of nodes first select them and then click down on one of the selected nodes and drag it to its new position To change the shape of a link first select it by clicking on it then click down on it again and drag the cursor to the point where you want the link bend to be 1 A link can be disconnected by clicking on it to select it then clicking down on the hilited squa
43. acing of the grid to make it finer or courser do a Layout Grid Spacing menu command and a dialog box will appear allowing you to make the setting Sometimes it is useful to be able to move a node or set of nodes a small predictable amount You can use the arrow keys to do this nudging Simply select the nodes you wish to move and then press the key with the arrow in the direction you want them to move The distance they will be moved with each press of the key is the grid spacing providing the autogrid is turned on so you can adjust this amount using the Layout Grid Spacing menu entry If the autogrid is turned off then they will be moved the smallest perceptible amount with each press of the key 3 7 Reshaping a Link When network diagrams become large it can be very difficult to view them if all the links between the nodes are straight lines Even small diagrams can sometimes be made more legible by choosing suitable paths for the links To shape a link first click once on the link to select it The link will be drawn with the hilite color surrounding it Then click down again on the selected link and drag the cursor A bend will be placed in the link and dragged by the cursor You can repeat this to add as many bends as you wish To move the position of a bend first select the link as before The link will become hilited and there will be a square box at each of its bends and at its two endpoints To move a bend or an endpoint
44. alog box at once You can use the scroll bars to view whatever part of the list you are currently interested in The lt home gt lt end gt lt page up gt and lt page down gt keys may be used as well You can also resize the relation dialog box to make it bigger or smaller by clicking in the box at the lower right corner and dragging to the new size When you first bring up the relation dialog box it is constructed with a size to match the tables required for the node its for If you change which node the dialog box is for it is sometimes convenient to resize the dialog box as well so it better suits the tables of the new node 46 5 7 X Unspecified and Impossible Cell Values There are two special values which can appear in any cell of the relation table whether it is for a deterministic or probabilistic node One is a blank cell which means that the value of the cell has not been specified You may be building up a network over a number of sessions with Netica and you can use the blank cells to keep track of which parts of the relationships have not yet been determined New relations start out with all blank cells and you can set any cell or group of cells to blank by selecting the cells and then pressing the delete key or doing an Edit Delete menu command If the node is deterministic you can set a cell to blank by choosing Unknown from the pop up menu which appears when you click on the cell If you try to do inference w
45. alue finding maximized 54 experience 72 73 explaining 26 explaining away 9 F12 key 28 F9 F11 keys 27 fading 75 degree of 76 familiarity assumed 6 features of Netica 7 file format belief network DNET 1 31 case file CASE 1 67 File Close menu command 27 36 46 File Get Case menu command 65 File New Network menu command 27 58 File Open menu command 27 File Print menu command 81 File Printer Setup menu command 34 81 File Quit menu command 9 File Save As menu command 27 31 File Save Case As menu command 65 File Save menu command 27 31 filling in missing node probabilities 49 findings 19 22 consistency 24 independent 24 likelihood 24 negative 23 order of entry 22 positive 23 reading from file 65 removing 22 66 retracting 22 saving to file 65 sets of 65 transferring networks 66 findings pop up menu 22 fixed decision function 55 Flow Instrument example 56 58 folder of examples 8 font 78 forgetting 53 75 frequency of cases 68 function inversion 60 functional relation 18 fuzzy logic 72 generating random cases 68 generating random node relations 49 generating uniform node probabilities 49 getting started 6 grid spacing 30 group decision making 55 Heckerman amp MW95 16 83 Heckerman93 83 Henrion amp BH91 16 83 Hidden node style 78 hiding links 80 home key 34 46 icon large blue square 8 IDname 36 IDnum 68 ignorance 72 imperfect ob
46. ampling error in converting the equations to probability tables You may also want to try a finer discretization by changing the Ranges That ends our quick tour of Netica Now you will probably want to explore some aspect of Netica in more detail by reading the appropriate chapter If you wish to learn more about belief networks or influence diagrams the next section should get you started 1 5 Introductory References for Belief and Decision Networks For an overview of belief and decision networks there are two special journal issues that are suitable The first is the winter 1991 edition of AJ Magazine which contains Bayesian Networks Without Tears Charniak91 and Decision Analysis and Expert Systems Henrion amp BH91 The other is volume 38 of the Communications of the ACM which is devoted to belief and decision networks Heckerman amp MW95 and has introductory material and descriptions of real applications Complete references for all the books and papers discussed here can be found in the bibliography 16 For a very good concise but in depth examination of belief networks the theory behind them and the algorithms Netica uses for inference read Spiegelhalter amp DLC93 It concentrates on medical diagnosis but the ideas are widely applicable It examines some advanced aspects of the theory and algorithms but is okay for a beginner who can just skip a few of the sections Although much of the literature on belief net
47. and enter the probabilistic relationships between them Then use File Open to open the library file with the instrument node Select that node do an Edit Copy then click in the application network where you want the instrument node to appear Do an Edit Paste click again where the other copy of it should be and do another Edit Paste Finally hook up each of instrument s disconnected links to their appropriate nodes using the method described in the previous section Now the application network is ready for probabilistic inference you can do a Network Compile menu command Perhaps you have positive findings for the instrument node i e what you read from its dial and you 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 As a sister product Netica Programmer s Library API can be useful for automating the process of constructing networks that are composed of nodes or subnetworks from a library perhaps by using templates or rules 59 8 Transforming a Network There are certain ways that Netica can transform a network model which modifies its representation without modifying its meaning Netica can remove nodes and reverse the direction of links in such a way that any inference done with the resulting network yields precisely the same results as the original network excep
48. assword 8 pasting into other applications 80 pasting nodes 33 Pearl88 17 84 plan 51 policy 51 Political Riding example 66 positive finding 23 posterior probabilities 19 prediction 70 printing 81 89 multiple pages 81 prior probabilities 19 probabilistic causal network 18 probabilistic inference 19 20 by node absorption 63 probabilistic vs deterministic node changing 46 probabilities don t sum to 1 25 49 probability 72 Qi amp Poole95 84 Q194 84 query node 62 70 quick tour of Netica 9 quitting Netica 9 random cases 68 random node relations 49 Ranges edit box of node dialog box 38 ranges of node 38 41 real number findings 66 reconnecting links 33 58 redoing 29 references for BNs 16 83 relation dialog box 43 Apply button 45 arrow keys 45 blank cells 47 cell of 44 changing cell values 45 Close button 46 closing 46 cutting and pasting 48 Determin Chance selector 46 empty cells 47 example 44 Load button 45 multiple 50 navigating cells 45 obtaining 43 Okay button 45 page down key 46 page up key 46 Relation menu commands 48 resizing 46 scrolling 46 selecting cells 48 switching node 45 tab key 45 undoing 45 x cells 47 Relation Check menu command 49 Relation Fade menu command 75 Relation Fill in Missing menu command 49 Relation Incorp Case File menu command 72 Relation Incorporate Case menu command 71 Relation Nor
49. be the same except you may substitute space s and or a comma for each tab and linefeed s for carriage returns if you wish Blank lines will be ignored 48 5 9 Relation Menu Commands While working in a relation dialog box the Relation menu is often useful First you select some cells you wish the menu command to apply to and then choose the command from the menu For most of the commands if no cells are selected the command is applied to all the cells of the dialog Relation Fill in Missing enters a probability into blank cells so that the probabilities of each selected row add up to 1 0 i e 100 Any row having no blank cells more than one blank cell or impossible values will simply be ignored Using the tool bar button with the tiny number entering the small blue empty cell is another way to do this command Relation Normalize will make sure that the probabilities of each selected row adds up to 1 0 i e 100 by dividing each number by the sum of the row Any row having unspecified or impossible values will simply be ignored This command is useful if you want to enter probabilities as decimal fractions e g 0 25 rather than percentages e g 2596 After you enter all the numbers simply normalize them and they will be converted to percentages The normalize command can also be done using the tool bar button with the large 1 in it Relation Uniform Probabilities will set the selected rows of a probabilist
50. cating 33 equation 40 font 78 input names 40 kind 37 link delay 40 moving 30 name 34 36 66 77 pasting 33 ranges 38 41 relationship with parents 43 removing states 38 size 78 state values 39 states 38 40 title 36 title displayed 77 type 36 when changed 42 node absorption 62 88 for probabilistic inference 63 order of 62 to maximize expected utility 54 node dialog box 35 Apply button 35 Close button 36 Cont Discrete selector 36 Delete button 38 Kind selector 37 Load button 35 multiple 50 Name edit box 36 Nature Dec selector 37 New button 38 obtaining 35 Okay button 35 parent selector 40 Ranges edit box 38 State Value edit box 39 States edit box 38 Title edit box 36 node libraries 56 node styles 78 Belief Bars 78 Belief Meter 79 Circle 78 default 78 Hidden 78 Labeled Box 78 no forgetting links 53 64 nonmonotonic logic 72 normalizing node probabilities 49 Norsys address 2 6 not enough memory 53 nudging links 31 nudging nodes 30 NumCases 68 Okay button in node dialog box 35 in relation dialog box 45 operations research 17 optimal decisions 51 Optimize Decisions menu command 53 optimized compiling 21 other state 79 other state reading case 66 overlapping characters 81 page breaks 81 page down key 34 46 page size 81 page up key 34 46 Paint pasting to 81 parameter learning 70 parent node 18 p
51. ce diagram evaluation in Computational Intelligence 11 3 Russell Stuart and Peter Norvig 1995 Artificial Intelligence A Modern Approach Prentice Hall Englewood Cliffs NJ Shachter Ross D 1986 Evaluating influence diagrams in Operations Research 34 6 871 882 Shachter Ross D 1988 Probabilistic inference and influence diagrams in Operations Research 36 4 589 604 Shachter Ross D 1989 Evidence absorption and propagation through evidence reversals in Proc of the Fifth Workshop on Uncertainty in Artificial Intelligence Windsor Ont 303 308 Later republished in Henrion Max ed 1991 Uncertainty in Artificial Intelligence 5 North Holland Amsterdam Smith James E Samuel Holtzman and James E Matheson 1993 Structuring conditional relationships in influence diagrams in Operations Research 41 2 280 297 Spiegelhalter David J A Philip Dawid Steffen L Lauritzen and Robert G Cowell 1993 Bayesian analysis in expert systems in Statistical Science 8 3 219 283 Zhang Lianwen Nevin 1993 A computational theory of decision networks PhD thesis Dept of Computer Science Univ of British Columbia BC Canada Also released as Tech Report 94 8 Dept of Computer Science Univ of British Columbia BC Canada Zhang Lianwen Nevin Runping Qi and David Poole 1994 A computational theory of decision networks in International Journal of Approximate Reasoning 1
52. cess of building the decision network clarifies the problem often slowly changing your gut feeling as you proceed and the iteration process forces you to re examine assumptions you have made In a group decision making environment constructing a decision network is often of great benefit in fleshing out the differences in people s beliefs and values and allows people to discuss specifics rather than arguing in generalities Also once the policy is formed the decision network acts as a living document of the beliefs and values that lead to it If those change over time the decision network can be changed to generate a new policy Or parts of it can be copied and pasted into new networks for new decision problems If a policy results in a bad outcome it is possible to go back and determine whether it was based on bad information and if so to change that information for the next decision making situation 6 5 What if Decision Analysis With Netica s undo feature it is easy to solve a decision network undo it change a utility value or a node relationship and then re solve the network to see how the optimal decisions and maximum expected utility are affected But what if you want to force a decision node to have a certain decision function and see how the other decisions and maximum expected utility change Just enter the desired decision function for the node in its relation dialog box or paste it in since you are often obtaining it
53. click down in its hilited box drag it to its new position and then release the mouse UE button Moving one bend into another or into an endpoint will combine them which can be used to remove bends There are some special considerations when moving the endpoints of a link The arrow end of a link can not be dragged very far from the node it points to if you try to the arrow will just bump against an invisible barrier This prevents the creation of misleading looking diagrams since the link is still considered to be connected to the node If you drag the non arrow end of a link too far from its parent node then the link will become disconnected from that node You can tell this has happened because the name of the link will suddenly appear at the endpoint you have moved See section 7 1 for more information on this If the autogrid is on there is a check mark in front of the Layout AutoGrid menu entry then the endpoints and bends of a link will always be placed on grid positions after a move This makes it easy to quickly draw network diagrams with aligned link segments and to make some segments perfectly horizontal or perfectly vertical You can turn the autogrid on or off by choosing the Layout AutoGrid menu entry and set the spacing of the grid with Layout Grid Spacing If you have just been moving a link bend or endpoint and the link is still selected you can nudge that bend or endpoint a little to get it exactly wh
54. clicking on the node When you make changes in the dialog box they won t actually be applied to the node until you click the Apply or Okay buttons It is possible to open dialog boxes for a number of nodes at the same time and even to open more than one box for the same node There is a whole chapter devoted to using these dialog boxes so here we will just mention a few things You can change a node s name or title in the obvious way by typing in the appropriate text field of the dialog box To change the name of one of the node s states choose the state using the selector beside the State label and then type in the neighboring text field You can add or delete states with the New and Delete buttons Most people find it more convenient to enter or change state names using the text entry area at the bottom of the dialog The text entry area at the bottom of the dialog can be used to enter or change several different things you choose the thing to work on with the selector directly above it For instance to enter some text documenting the node you choose Description from the menu and then type it in the text entry box Some choices such as When Changed can t be modified and are for viewing only In order to change the probabilities of a node conditioned on the values of its parents first open the node s relation dialog box as described in the previous section You can click on a No number or stat
55. copied to it using Edit Copy and Edit Paste which can transfer material from one network to another and also copies all the links between nodes in a subnetwork When a node is being duplicated but one of its parents isn t then the duplicated node will have a disconnected link where that parent was To use nodes in the library you use Edit Copy and Edit Paste again this time to duplicate from the library into the new network Then you connect up any disconnected links as described in the section above before compiling the network or using it for inference For example to create a library with just the instrument node of figure 6 1 first you would make a network with the 4 nodes flow rate temperature instrument status and instrument Put links from nodes flow temperature and instrument status to instrument Enter a probabilistic relationship for the node instrument Now make a new network with File New Network select the instrument node in the original network do an Edit Copy click in the new network do an Edit Paste then a File Save You now have file which is a library with a single node in it 58 At a later session you can use the library to construct a network in which the instrument is used to measure the flows as described at the beginning of this chapter Make a new network with File New Network add the nodes flow1 flow2 instrument status and room temp link them together as shown in figure 6 2
56. de by choosing Likelihood from its findings pop up menu You will then be queried for the likelihood numbers You can enter a negative finding by entering a likelihood finding consisting of all 1s except a single O for the state that you know it s not Whenever you enter a positive finding for a node all the old findings for that node are automatically retracted first However if you enter more than one likelihood finding for a node you will be queried if you first want the previous finding s to be removed or if you want them to accumulate By letting them accumulate you can enter several independent pieces of evidence e g imperfect observations for the same node If they are not independent and it is too inaccurate to approximate them as independent then they should be entered by adding child nodes to the observed node one for each observation connecting them together to show the dependency and then entering positive findings for the child nodes 2 8 Consistency If you enter several likelihood findings for the same node letting them all accumulate then Netica checks to make sure they are consistent and displays a message if they aren t The only way they can be inconsistent is to have a negative finding or zero likelihood for every state of the node 24 Checking for consistency between the findings of one node and those of another node given the inter node relations encoded in the network can only be done by belief u
57. ding 49 row will be hilited and a message displayed indicating the problem This command can also be done using the tool bar button with the black check mark Many of these commands can also be done from the network window without using any relation dialog by selecting the nodes of interest and then choosing the menu command from the Relation menu It will apply to the entire relationships of all the selected nodes 5 10 Multiple Dialogs for One Node You may have more than one relation dialog box or node dialog box for the same node This can be confusing if you are not careful so it is not recommended unless you need it However in some situations it is very useful Each dialog box stores all the settings for its node and doesn t loose them when you make changes in another node dialog box or to the node itself unless you press the Load button So you can have several different settings for a node one set in each dialog box and alternate between them just by pressing the Apply button on the dialog box of choice Of course you can do all kinds of other operations in between such as compiling the network saving it to a file making queries etc You open multiple dialogs for a node in the same way as you open a single dialog Just do the action repetitively without closing the previous dialogs first and answer no to the question of whether you want to bring the existing dialog to the front 50 6 Decision Proble
58. e involved It has an IDnum column but no frequency column gt CASE 1 gt IDnum VisitAsia Tuberculosis Smoking Cancer TbOrCa XRay Bronchitis Dyspnea 1 o_Visit Present Smoker Absent True Abnormal Absent Present 2 o_Visit Absent Smoker Absent False Normal Present Present 3 o Visit Absent Smoker Present True Abnormal Present Present 4 o Visit Absent NonSmoker Absent False Normal Absent Absent 5 o_Visit Absent Smoker Present True Abnormal Present Present 6 o_Visit Absent Smoker Absent False Abnormal Present Present 119 o_Visit Absent Smoker Absent False Normal Present Present 120 o_Visit Absent Smoker Present True Abnormal Present Present Here is another example of a case file this time for cars brought into a garage notice BatAge which is a continuous variable CASE 1 Starts BatAge Cranks Lights StMotor SpPlug MFuse Alter BatVolt Dist PlugVolt Timing False 5 49 False off a fouled okay dead E good False 138 False off x okay okay dead F none bad False 572 False off Okay okay okay Okay dead Okay none good True 4 1 True bright sid okay okay strong Okay strong a True 2 4 x bright A wide okay x strong Okay ui s True bright fouled okay Okay strong good False lo True off Okay okay okay Okay dead ri none good True 239 True bright K strong Okay strong Future versions of Netica will support more advanced operations with cases including a more efficient file r
59. e window in the direction you wish to scroll The further you go outside the faster it scrolls The area within which you can create a network diagram is a rectangle of limited size Once you scroll to the end of it you cannot scroll any further and you cannot put any nodes outside of its boundaries You can change the size of this area with the Layout Drawing Size menu command If you increase the size of the window larger than the current drawing size then the drawing size will be automatically increased including maximizing a window The size of the page can be adjusted with the File Printer Setup menu command and is based on how much your printer puts on one page There is more information on pages in section 11 6 Printing 34 4 Changing Node Characteristics We have seen how you can add or delete nodes or links by using menu commands and the tool bar However to change the characteristics of a node e g its name or how many states it has you need to use what is called the node dialog box If you want to change the way a node is related to its parents e g its conditional probabilities you use the relation dialog box which is described in the next chapter 4 1 Obtaining the Node Dialog Box The easiest way to obtain the node dialog box for a node is to double click on the node Another method is to select the node and then press the lt Enter gt key This last method is especially useful when adding new nodes to t
60. e library twice into the new network and graft it to the appropriate nodes in that network see diagram 6 2 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 by Figure 7 2 A network which was built to analyze an instrument measuring the flows in 2 different pipes in the same room using the instrument node from the library depicted in figure 7 1 instrument_status 7 1 Disconnecting and Reconnecting Links A link may be disconnected from its parent node without the link actually being removed That means that the child node can maintain the information on the conditional probability relation it had with its parent without actually being connected to the parent The intention is that later it will be reconnected to the parent or more likely to some other node before it is used for inference To disconnect some links select them and then click on the knife tool bar button or do Modify Disconnect Links Each link will turn into a short stub connected to its child node and labeled with the name of the link If you have not previously named the links see section 51 4 10 3 then Netica will name them with the names of the parent nodes The disconnected links will look similar to the lin
61. e name if it s a deterministic node to change it If no probabilities have yet been entered for this node you can click on an empty cell to enter a number The numbers must be entered as percentages You can select some cells by clicking down in a cell that is not currently being edited and dragging to enclose the cells before releasing the mouse button You can select whole rows at a time by clicking and dragging slightly to the right of the double vertical line this is how you must select deterministic cells since clicking directly on them brings up the state menu There are several commands in the Relation menu that you can use to set the values of selected cells such as Uniform Probabilities Fill Missing Normalize and Randomize Any changes you make in the dialog box will not actually be transferred to the node until you press the Apply or Okay button These two buttons do the same thing but the Okay button also removes the dialog box Node absorption removes a node without effecting the overall global relationship of the rest of the nodes i e the joint probability distribution Here is a small demonstration of node absorption showing how it doesn t effect the beliefs of the rest of the network Open Car Diagnosis 2 Compile it with Network Compile and notice that the belief is 25 4 that Spark Quality is good If you enter a finding of dim for node Headlights the belief changes to 1 47 Now select node
62. e 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 need 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 Suppose you are now going to sequentially draw a number of balls from the bag If you drew 3 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 white balls In the second situation your probability of the next ball being white should be less than 0 5 because you know that now there are more black than white balls left in the bag 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 probabili
63. e toolbar button Selecting a node or nodes and doing a Modify Disconnect Links command will disconnect all links entering the node s A disconnected link turns into a short stub connected to the child node and labeled with the link name This will be the name you gave it previously see chapter 4 Changing Node Characteristics or if you never did it will be the name of the old parent node If you want to disconnect a link without loosing all its bends click on the link to select it then drag the hilited box at the tail of the link far enough away from the parent node and release the mouse button You will know that you dragged it far enough if the link name appears at the tail of the link after releasing the mouse button A link cannot be disconnected from its child node That would not make sense since a disconnected link is really just a parent place holder to maintain the node s relation e g conditional probabilities until it is connected up to a new parent To achieve the affect of uade disconnecting a link at the child end it sometimes makes sense to do a link reversal see link reversal and then disconnect the link at the parent end To connect a disconnected link to a new parent click on the link to select it then drag the hilited box at the tail end of the link over the node you wish to connect it to and release the mouse button A link can be disconnected from one parent node and reconnected to a new parent in
64. e while you are changing the table and you haven t yet pressed the Apply button you can revert to the original node by clicking on the Load button if you have already pressed the Apply button you should make the network window active do an Edit Undo command then go back to the relation dialog and click on Load The second use for the Load button is to update the relation dialog after something else has changed the relation at the node For example you might be solving a decision network repeatedly while varying some part of it After each solution you want to see how the optimal decision function has changed You would bring up the relation dialog box for the decision node of interest leave it up and after each re solution of the network you would click on the Load button to observe the changes in the tables Another example could be that you are having Netica learn a belief network from a number of case files and you want to observe how the conditional probabilities change as the learning process continues You can switch which node a relation dialog box is for by using its pop up menu labeled Node From this menu you can choose any node in the network and when you do the contents of the dialog will be completely re adjusted for the new node If you had made changes 45 in the dialog box before switching nodes and had not yet pressed the Apply button then a message will be presented asking if you want to apply the chan
65. elate any proposed machine learning method to a Bayesian method to better understand its assumptions strengths and weaknesses If it can be cast at least approximately into a form of Bayesian learning then you can check to see if the prior probabilities are suitable for the problem If it does not even roughly correspond to any 74 form of Bayesian learning then its results are probably not very accurate and it should not be used unless it has other valuable qualities such as being particularly simple or fast Using the equations of the previous section is equivalent to a system of true Bayesian learning under the assumptions that the conditional probabilities being learned are independent of each other and the prior distributions are Dirichilet functions if a node has 2 states these are beta functions For more information see Spiegelhalter amp DLC93 section 4 1 with the word precision equivalent to our experience Assuming the prior distributions to be Dirichilet generally does not result in a significant loss of accuracy since precise complex priors aren t usually available and Dirichilet functions can fairly flexibly fit a wide variety of simple functions Assuming the conditional probabilities to be independent generally results in poor performance when the number of usable cases isn t large compared to the number of parent configurations as mentioned at the beginning of this chapter 10 4 Fading Wh
66. en a belief network 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 might be an adaptive belief network that 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 select the nodes to be faded do a Relation Fade menu command enter a degree from 0 to 1 and it will reduce the experience and smooth the probabilities of the node by an amount dictated by the degree with 0 having no effect and creating uniform distributions with no experience Fading once with degree 1 d and again with degree 1 f is equivalent to a single fading with degree 1 df 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 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 75 When learning in a changing environment you would normally fade every once in a while so that what has been recently learned is more strongly weighted t
67. en the two perhaps based on previous observations Forecast Weather Umbrella Satisfaction 2 There is a link from Forecast to Umbrella indicating that the decision maker will know the forecast when he makes the decision but no link from Weather to Umbrella if he 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 he is most happy when it is sunny and he doesn t take an umbrella utility 100 next most when it is raining and he takes an umbrella utility 70 He hates carrying an umbrella on a sunny day utility 20 but is most unhappy if it is raining and he doesn t have one utility 0 6 1 Constructing a Decision Network Constructing a decision network is pretty much the same as constructing a belief network so most of the material in chapters 2 3 and 4 is applicable One difference obviously is that you must designate some nodes as decision and utility nodes Usually you do this when you first add them by using the tool bar button with the blue rectangle to add decision nodes and the one with the green hexagon to add utility nodes However you can change node kinds using the node dialog described in chapter 4 obtained by double clicking on a node You can also change node kinds by selecting the nodes you wish to change and then clicking on the tool bar butt
68. epresentation and a way of using belief networks as indexing functions to do the kind of lookup common in case based reasoning However the above described type of file format will always be supported as well 9 3 Generating Random Cases You can use Netica to generate a series of random cases whose probability distribution matches that of a particular belief network which is sometimes known as sampling These cases can by 68 used as example scenarios of what one should expect if the belief network matches reality Or they can be manipulated and combined with other cases and then used to learn a new network The cases will be stored in a file whose format matches the specification of a case file as described in the previous section The sampling algorithms used are precise so that the long range frequencies of the cases will exactly approach the probabilities of the belief network If you have used an equation to define the relation between a node and its parents then that equation will be used to generate the random cases not any probability table which approximates the equation Continuous variables which have been discretized will be provided with a continuous real number in each case not just a state representing a range of values To generate the case file make sure the belief network to be used is the active window select the nodes for which you wish to have values in the case file and then do a Network gt Generate Cases
69. er influence diagram It involves two sequential decisions about whether to do some tests and then whether to buy a certain used car The optimal decisions turn out to be not to do any tests D none but to buy the car B Buy when D none 6 4 Model Iteration For some applications of decision networks especially in areas like gambling control or automated decision making it is relatively easy to set up the relations to suitably reflect reality and the decisions that the network makes are much better than decisions you would make unaided because of Netica s superior ability to reason precisely with probability and to deal with many interactions in very complex situations However for other applications especially in areas like business decision making or public policy the decisions that Netica makes may not match your gut feelings and you may suspect that Netica is wrong In that case usually the decision network doesn t capture the decision 54 problem well enough The usual procedure is to go back to the decision network model change it to more accurately reflect reality and solve it again Then repeat the process until you are satisfied with the results But of what use is the decision network if all you do is try to get it to match the decisions you would make anyway Professional decision analysts who use decision networks on a regular basis tell us that they are invaluable for disciplined decision making The pro
70. eral one 49 right arrow 23 scissors 32 star 62 X over green relation tree 49 Xed case symbol 22 update beliefs 23 utility node 27 37 52 toolbar buttons missing 8 trademark notices 2 transferring cases between networks 66 transferring nets between computers 31 transforming a network 60 triangulated network 80 type of node 36 Type selector of node dialog box 36 Umbrella example 52 uncertainty 72 Uncertainty in AI Conference 17 undoing 29 uniform node probabilities 49 uninstalling Netica 8 unique node names 34 unlearning 71 unspecified probabilities 47 Untitled x window title 31 Update tool button 23 utility node 37 51 utility node tool 27 37 52 value node 37 51 variable 18 version number 6 virtual evidence 24 weak links 61 Weather example 56 what if analysis 55 9 when changed node 42 wild state reading case 66 Window menu 27 Windows menu 35 43 Word 97 pasting into 81 word processor copying to from 48 66 wrong decisions 54 x cells in relation dialog box 47 Zhang amp P96 84 Zhang amp QP94 84 Zhang93 84
71. ere are several different forms in which a node can be displayed and these are known as node styles There is a default style for the whole network but each node can be set to its own style individually which overrides the default To set the default style for the network make sure no nodes are selected when you choose that style from the Style Node menu To have some nodes override that style select them and then choose the desired style from the menu If you have given some nodes an overriding style but now you want them back to the default style select them and then choose Style gt Node Default If you use the menu to change the default node style of the whole network but none of the nodes change it is because they all have overrides to the default To remove these overrides you could select them all and then choose Style 2 Node Default The various node styles are Labeled Box Hidden Circle Belief Bar and Belief Meter Labeled Box style draws a box whose shape and color are determined by the node kind with the name title of the node written within it Hidden style draws nothing and Circle style draws the node as a small circle Belief Bar and Belief Meter styles are described in detail below 11 3 1 Belief Bar To display the belief levels of a multistate nature node the belief bar style is most useful It is illustrated in figure 11 1 Nodes can by displayed in this style by selecting them and then choosing Style gt N
72. ere you want by pressing the appropriate arrow key With every press of the key it will move a distance of the grid spacing if the autogrid is on or the minimum perceptible distance if the autogrid is off 3 8 Saving a Network to a File To save a network to a file make sure its window is the active one by clicking in it or choosing it from the Windows menu and the do a File Save As command You will be prompted for the file name and what directory to place it in After you have saved a network its window title will no longer be Untitled x where x is some number but instead it will be the name of the file saved to without a terminating dne or dnet Then you can save it subsequent times using the File Save command without being prompted for the name If the File Save command is dimmed that means that the network has not been changed since it was last saved or read and so the screen version is the same as the file version The network gets saved to a file consisting only of ASCII text so it may easily be transferred from one type of computer to another e g from Windows to Unix to Macintosh or sent by email You may examine and modify the file with a text editor It is in the DNET 1 file format so it contains DNET 1 somewhere in the first 3 lines A document precisely Eus describing the DNET 1 file format is available from the Norsys WWW site called DNET File Format txt 3 9 Deletin
73. g Nodes and Links To delete a node or nodes first select them and then press the delete key or do an Edit Delete command from the menu This will remove the nodes and all links from other nodes going to them Links going from them to their child nodes will be disconnected just before the deletion see section 7 1 These disconnected links will be selected after the nodes are removed so you can easily delete them as well by just pressing the lt delete gt key a second time If you wish to remove the nodes but maintain the global relationship of the remaining nodes 1 e the joint distribution see the Network Absorb Nodes command To delete a link click on it to select it and then press the delete key or do an Edit Delete command from the menu To delete a series of links select them all and then press the delete key When a link is deleted the conditional probabilities of the child node are collapsed to eliminate their dependence on that parent as if the parent took on its first state When a link is deleted the parent node is not affected in any way 3 10 Disconnecting and Reconnecting Links If you wish to disconnect a node from one of its parents without modifying its conditional probabilities perhaps to put it in a library or to connect it to a different parent the link between them may be disconnected To do this select the link or links and do a Modify gt Disconnect Links command or click on the knif
74. g it the active window and then doing File Close 10 1 4 2 Network Construction and Transformation Do File New to create a new belief or decision network window To add a nature node i e a chance node or deterministic node move the cursor to the tool bar and click on the button with the yellow ellipse When you return the cursor to the new window it will change to an ellipse and when you click in the window a node will be added at the cursor The node will be selected when first added i e displayed with inverted colors so by pressing the lt Enter gt key a dialog box will be opened for changing node attributes You can use this to enter the name title etc of the node Utility nodes also known as value nodes or decision nodes may be added in the same way as nature nodes by using the green hexagon or blue rectangle tool buttons respectively Links may be added by clicking on the tool button with the downward pointing arrow not the upward arrow then clicking on the node you want the link to come from i e the parent node and finally clicking on the node you want it to go to i e the child node Alternately you can click down in the parent node and while holding the mouse button down drag the cursor to the child node and then release it If you double click on a tool bar button then it will create a cursor that you can use to add several nodes or links without it switching back to the pointer e
75. ge the font and size of all the nodes at once 13 1 4 3 Case Files Open the belief network called Car_Diagnosis_0 It is a simplified example network containing nodes for a few variables of interest when diagnosing a car that is not running The nodes are linked up in a causal manner but the network does not contain any information other than the node names their states and how they are linked You can use a relation dialog box to examine a few nodes to verify that they have no probability tables To learn a probabilistic relation for each of the nodes we will use a file of fictitious cases of cars previously arriving at a garage called Car Cases You may want to examine this file with a text editor The row of headings across the top are the names of the nodes in the network and each possible value they can take are the state names of those nodes BatAge is a continuous node so its values are real numbers The asterisks indicate data values which are not known i e missing data Make sure that the network window is the active window and that no nodes of the belief network are selected otherwise the learning will only apply to the selected nodes and then do Relation Incorp Case File When you are queried for a file choose Car Cases and enter 1 for the degree Netica will use the cases to learn probabilistic relations for each node of the network with the Message window displaying the fraction completed
76. ges before switching nodes If you click on the Close button or in the relation dialog s go away box on the left end of the title bar or do a File Close menu command while the dialog is the active window the dialog will be removed If you previously have made some changes in the dialog and haven t pressed the Apply button Netica will ask if you want to apply those changes to the node before removing the dialog 5 5 Deterministic Chance Pop Up The relation dialog box has a selector that allows you to make a nature node deterministic or probabilistic i e a chance node If you use this selector before you have entered anything into the table cells it will just modify the dialog box to be suitable for entering deterministic or probabilistic information If you have already entered a relation that relation will be converted Converting a deterministic relation to a probabilistic representation is simple each row of the result will consist of all 0 entries except one 100 entry at the state the original deterministic function mapped to Converting a probabilistic relationship to a deterministic one generally looses some information For each parent configuration the function output will become the state that was most likely in the probabilistic relation 1 e had the highest conditional probability 5 6 Scrolling and Resizing Since a node may have very many parent configurations they often won t all be visible in the relation di
77. han what was learned long ago If an occurrence time for each case is known and the cases are learned sequentially through time then the amount of fading to be done is degree 1 rAt where At is the amount of time since the last fading was done and r is a positive 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 76 11 Display Style and Printing The Style menu allows you to change the way networks are displayed and printed without changing what they mean or the way they behave The size and font of the nodes and link labels can be adjusted and individual nodes can be displayed in a manner which is best for that node If an end user who is not familiar with belief networks is going to be using the finished network then it can be displayed in a suitable manner perhaps by hiding links and some nodes and displaying the rest of the nodes as bar graphs meters or data entry ovals depending on the application Network diagrams can be printed with a printer in color and magnified reduced if desired Presentation quality graphics can be created by copying and pasting from a network into other applications 11 1 Node Name and Title Display Every node has a name but there are character and length restrictions on names see section 4 3 To provide you with greater flexibility in labeling nodes some or all of the nodes can als
78. hange the real number associated with a state 4 10 Multi Purpose Box At the bottom of the node dialog box is a text edit box with a selector above it This box is used to view or enter several different characteristics of the node and the selector is to choose which characteristic to view or enter This selector is known as the node dialog box s multi purpose selector and each of the section headings below corresponds to one of its choices To scroll in the text edit box click down within the box and then drag the cursor in the direction you wish to scroll or use the arrow keys to attempt to move the cursor past the box s boundary If you have a very large amount of text it is probably best to just paste it in from a text editor 4 10 4 Node Description When a node dialog box s multi purpose selector is set to Description you can enter or view the description of the node The description is an unrestricted block of text which can be used to store whatever information about the node you wish such as its meaning the meanings of its 39 states how it is to be measured the origin of its probabilities copyright information etc The description can be as long as you wish 4 10 2 Node Equation When the multi purpose selector of a node dialog box is set to Equation you can view or enter the probabilistic or deterministic equation that provides the relation between the node and its parents See chapter 12 Equati
79. he network since when a node has just been added it is already selected and you just have to press the lt Enter gt key You may have several node dialog boxes on the screen at the same time and you may alternate between using different node dialog boxes and directly working in the network window Each node dialog box pertains to a single particular node In fact you can even have more than one node dialog box for the same node see section 5 10 Multiple Dialogs for One Node 4 0 Making Changes Whenever you make any changes within the node dialog box they don t actually affect the node until you click on the Apply or Okay buttons Then all the settings are transferred to the node in the network The only difference between the Apply and Okay buttons is that the Okay button removes the dialog after transferring the settings while the Apply button doesn t Clicking on the Load button will make all the settings in the dialog box the same as the node in the network 3S If you click on the Close button or in the dialog s go away box on the left end of the title bar or do a File Close menu command the node dialog will be removed If you previously have made some changes in the dialog box and haven t pressed the Apply button Netica will ask if you want to apply those changes to the node before removing the dialog box 4 3 Node Name You can change the name of a node using the Name text edit box of the node s dialog box
80. her type of computer Nodes are not required to have titles If a node does not have a title then anytime that Netica would normally use a title it will use the node s name instead 4 5 Node is Discrete or Continuous The node dialog box has a selector with the values Continuous and Discrete which allows you to choose whether the node represents a continuous or a discrete variable A discrete variable is one with a well defined finite set of possible values called states Examples are the 36 number of dimes in a purse a statement which is either true or false which party will win the election the country of origin voltage output of a digital device and the place a roulette wheel stops A continuous variable is one which can take on a value between any other two values such as indoor temperature time spent waiting water consumed color wavelength and direction of travel A discrete variable corresponds to a digital quantity while a continuous variable corresponds to an analog quantity Often a variable will be continuous at one scale but discrete on another For instance the amount of water consumed might be discrete if you count individual water molecules but it is continuous at the scale we are concerned with Likewise the voltage output of a digital device might be discrete at the scale we are concerned with high amp low but continuous on a finer scale 0 7 3 5V and then discrete o
81. ic relationship to uniform probability vectors which means that all states of the child are equally probable So all the cells of these rows will contain the number 1 number of states expressed as a percentage Relation Randomize works on probabilistic or deterministic relationships For deterministic relationships it sets each selected cell to one picked randomly from the possible states of the node following a uniform distribution i e each state equally probable For probabilistic relationships it sets the cells of each selected row to randomly selected probabilities Of course the probabilities of each row will add to 1 0 i e 10096 The distribution of the probabilities entered is not uniform it favors numbers closer to 0 Using the tool bar button with the single die overlaid on the green relation tree is another way to do this command Relation Remove will convert all the selected cells to blank cells For an explanation of blank cells see section 5 7 above If there are selected cells then pressing the delete key will have the same effect This command can also be done using the tool bar button with the red X over the green relation tree Relation Check will check a probabilistic relationship to make sure all the probabilities are between 0 and 1 100 and that for each parent configuration i e row the probabilities add to 1 10096 A message will be displayed indicating the selected rows are all okay or an offen
82. ication reduction during printing 81 margins printing 81 Markov network 80 Matheson90 83 maximizing expected utility 51 medical domain 16 18 20 65 menu commands 20 menu items 8 Edit Copy 33 48 58 80 Cut 33 Delete 32 Duplicate 33 Paste 33 48 58 Redo 29 Select All 29 Undo 29 45 File Close 27 36 46 Get Case 65 New Network 27 58 Open 27 Print 81 Printer Setup 34 81 Quit 9 Save 27 31 Save As 27 31 Save Case As 65 Layout AutoGrid 30 31 Drawing Size 34 Grid Spacing 30 31 Show Page Breaks 81 Modify Add Node 27 Add Case File Nodes 72 Add Link 28 Disconnect Links 32 57 Network Absorb Nodes 62 Add No Forgetting Links 53 Automatic Updating 23 Compile 21 Generate Cases 69 Most Probable Expl 25 Optimize Decisions 53 Remove Findings 22 66 Update 23 Relation Check 49 Fade 75 Fill in Missing 49 Incorp Case File 72 Incorporate Case 71 Normalize 49 Randomize 49 Remove 49 Uniform Probabilities 49 View Edit 43 Style 77 Font 78 Net 80 Hide Links 80 Markov Net 80 Regular DAG 80 Triangulated 80 Node Belief Bars 78 Belief Meter 79 Circle 78 Default 78 Hidden 78 Labeled Box 78 Name 77 Name Title 77 Title 77 Title Name 77 Size 78 Window 27 35 43 Messages window 9 missing data 67 70 74 missing state reading case 66 missing toolbar buttons 8 model iteration 54 model search 61 Modify Add Node menu command
83. ifferent from the node s current number of states the node s number of states will be changed If you want to create a list of evenly spaced values there are a few shortcut methods you can use Each of the following special notations will expand into a list of numbers as described b e n will form a list beginning with b ending with e and having n ranges b e d will form a list beginning with b ending with e and each separated by d except the last separation may be less if e b is not evenly divisible by d b e L n will form a list beginning with b ending with e and divided logarithmically into n ranges b e d will form a list beginning with b ending with e each d percent bigger than the previous except the last may be less than d bigger if they don t fit evenly Note that if e is less than b then a decreasing list will be formed but n and d should still be entered as positive numbers The closing bracket may be replaced with a closing parenthesis if desired to indicate excluding the endpoint e from the list formed More than one of the above notations can be combined to form a longer list Here are some example entries one on each line 3 2 0 1 le4 infinity 0 10 10 0 10 1 10 20 2 20 30 3 33 37 dT s 1e6 1 L 6 200 10 15 4 10 7 When Changed When the multi purpose selector of a node dialog box is set to When Changed you can view the time and date the
84. ind optimal solutions using its powerful inference engine Many new features are currently under development and it will continue to be extended for years to come Characteristics Compiles belief Bayesian networks into junction trees of cliques for fast probabilistic reasoning Has an optimizing compiler to generate good junction trees Can learn probabilistic relations from data Generates presentation quality graphics which can be transferred to other documents Provides easy graphical editing of belief networks and influence diagrams including cutting and pasting of nodes and networks without loosing their probabilistic relations many ways of displaying nodes bar graphs meters etc links with bends to keep complex diagrams orderly allows comments keeps track of author when changed etc for each node unlimited levels of undo redo Can find optimal decisions for sequential decision problems i e later decisions are dependent on the results of earlier ones Can reverse individual links and sum out nodes of influence diagrams or belief nets for model exploration e Supports disconnected links which makes possible libraries of probabilistic relationships Has facilities to enter and update individual cases store them in their own files and apply them to other belief networks Allows the entry of probabilistic relations by equation with an extensive built in library of probabilistic functions and
85. ing belief updating at all There is a danger to keep in mind Even though the reduced network has fewer nodes than the original internally it may actually be more complex sometimes much more complex if many links were added during node absorbing or link reversing 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 query and evidence nodes is very small the resulting network must be simpler although the transformations to generate it might temporarily require a lot of memory 8 3 Probabilistic Inference by Node Absorption From the previous section you may have realized that it s possible to do probabilistic inference using node absorption by entering all the findings and then absorbing all the nodes except for a single query node The resulting probability relation for that node will be a single belief vector because the node won t have any parents that is the same as the belief vector that would be obtained by compiling the belief network and doing belief updating
86. isions and create probabilistic expert systems It is suitable for applications in the areas of diagnosis prediction decision analysis sensor fusion expert system building reliability analysis probabilistic modeling and certain kinds of statistical analysis and data mining This guide is for Netica Application it is not a manual for the Netica Programmer s Library also known as the Netica API Application Program Interface The API is a module with much of the same functionality as Netica Application but designed for programmers to embed in their programs This guide is for software version 1 05 you can check your Netica software for its version number by choosing About Netica from the Help menu It is only for the Windows version of Netica Application If you are using the Macintosh version there is a separate guide for that This guide assumes that you are familiar with using a computer running the Microsoft Windows operating system It also assumes familiarity with Bayesian belief networks or influence diagrams although it is very suitable for someone who is just in the process of learning about them Questions and comments about material in this document may be sent to norsys_info norsys com 1 1 Netica Application The Netica Application is a comprehensive tool for working with Bayesian belief networks and influence diagrams It can build learn modify transform and store networks as well as answer queries or f
87. ith a network which has some unspecified values Netica will not allow it and display a message The other special cell is one that has a single x in it This indicates that no value is required for the cell because that configuration of parent values will never occur It actually doesn t say anything about the relationship at hand but just that whoever was building the belief network didn t feel it was necessary to enter a value because in the context of the overall network it is not required If Netica is later doing inference and discovers that configuration of parent values can occur it will display a message alerting you If you put any arbitrary value in such a cell all inference results will be the same because the value will not be used The best value to put in the cell is the true value that would be applicable if the relationship between the parents was different but if that value doesn t exist or you don t know it or have time to determine it it is much better to use the x feature than to just put in an arbitrary value for three reasons First during inference Netica performs an important check for you as to whether the configuration is really impossible Second it documents your understanding at the time you were building the belief network for anyone else who later works with it Third if you later change other parts of the network or you cut and paste this node into a different application or put it in a network library those
88. ition or velocity so we delete them by clicking on each link to select it and pressing the delete key Then select the first two nodes and do a Relation Uniform Probabilities menu command This will give the first two nodes uniform probability distributions indicating we don t know anything about the initial position or velocity Finally we can compile the belief network for probabilistic inference with a Network Compile menu command Turn on automatic updating if it isn t already by choosing Network Automatic Updating so the menu item is check marked Experiment with setting the position or velocity by clicking on the desired range to indicate observations at certain times and see how the beliefs for position and velocity at the rest of the times change An interesting situation is when the ball is near the boundary but you don t know which way it is going since after a little while it will surely be moving away from the boundary perhaps due to a bounce Or if the positions at 2 times are known can it infer the velocity Or if just the velocities at two adjacent times are known and one is the negative of the other can it infer the position because it must have bounced You can also try entering some negative findings that the ball isn t at some particular position or velocity by holding down the shift key when you click on the range Remember that the numerical results will not be exact due to the discretization and s
89. itional probabilities of a node s relation to its parents This works very well when there is lots of data or nodes have few 70 parents but can result in under confidence and poor generalization otherwise Netica may not have seen some parent configuration so the learned probability distribution is uniform for it but Netica might do better if it assumed that parent configuration behaved similarly to other similar parent configurations i e assumed a little more independence between variables and a little less independence between conditional probabilities A future version of Netica will make it possible to not assume independence of the conditional probabilities if that is desired Netica will be able to learn relations from a set of special models It will also be able to suggest changes to the structure thereby partially doing structure learning 10 1 How To Do It There are two ways to learn probabilities from cases singly one by one or in batch mode from a file of cases 10 1 4 Single Case Learning To learn from a single case you must first have a network constructed Nodes in the network may already have their conditional probability relations which you entered manually or previously learned and which you now want to improve using learning On the other hand there might not be any conditional probability relations and you want to learn them from scratch For information on constructing the network see chapters 3
90. ks of the rightmost node in figure 6 1 If you want to disconnect all the links entering a node select the node and do a Modify Disconnect Links If you want to disconnect a link while maintaining its shape first click on the link to select it Then click down on the hilited box at the end of the link the end without the arrow and drag it away from the parent node When you release the mouse button you will know that you have dragged far enough if the name of the link appears beside it All of the bends of the link will be maintained To reconnect a disconnected link to a new node first click on the link to select it It will be outlined with the hilite color and there will be a box of hilite color at the disconnected end of the link Click down in that box drag it over the node that you want the link connected to and then release the mouse button If the connection was successful the name of the link will disappear If the node is not compatible with the original parent e g it has a different number of states then an error message will be displayed You may disconnect a link from one parent and connect it to a new parent in one motion if you wish 7 2 Making and Using Network Libraries Netica makes it easy to maintain libraries of disconnected nodes and subnetworks To make a new library just use the File New Network menu command Libraries are handled internally in the same way as regular networks Nodes and subnetworks can be
91. le Net submenu 80 Style Net Hide Links menu command 80 Style Net Markov Net menu command 80 Style Net Regular DAG menu command 80 Style Net Triangulated menu command 80 Style Node Title Name menu command 77 Style Node Belief Bars menu command 78 Style Node Belief Meter menu command 79 Style Node Circle menu command 78 Style Node Default menu command 78 Style Node Hidden menu command 78 Style Node Labeled Box menu command 78 Style Node Name menu command 77 Style Node Name Title menu command 77 Style Node Title menu command 77 90 Style Size submenu 78 sum of probabilities 1 25 49 summing out a variable 62 switching node of relation dialog box 45 synthetic data 68 system requirements 8 tab key in relation dialog box 45 terminating Netica 9 text editor copying to from 48 66 time node was changed 42 Title edit box of node dialog box 36 title of node 36 77 tool buttons absorb node 62 add link 28 chance node 27 37 compile network 21 decision node 27 37 52 disconnecter 32 disconnecter knife 57 edit view relation 43 fill missing probabilities 49 link reversing 61 normalize probabilities 49 randomize relation 49 remove findings 22 remove relation 49 shapes blue rectangle 27 37 52 die on relation tree 49 double arrow 61 down arrow 28 gray oval 27 37 green hexagon 27 37 52 green inverted V s 43 knife 57 lightening bolt 21 number enters blue cell 49 num
92. letters digits and underscores _ and it must be 30 or fewer characters long Also it must be different from the names of all other states of that node although it may be the same as a state name for a different node in the network To add a new state right after the current state click on the New button and to delete the current state click on the Delete button All discrete nodes must have at least one state but there is no upper limit to how many they can have Many people find it faster and easier to enter or change the states of a node using the Multi Purpose Box described in section 4 10 5 below instead of the previously described method 4 8 Node State Range If a node dialog box is for a continuous node then immediately below the state name edit box will be a couple of boxes labeled Range These are to provide threshold values for the ranges of each state in order to discretize the continuous variable see section 4 5 Node is Discrete or Continuous above This method of entering the discretization ranges is mostly just for touching up or to coordinate the ranges with state names but usually you will want to use the Multi Purpose Box described in section 4 10 6 below instead The box to the left is the lower end of the range for the current state inclusive and the box to the right is the upper end of the range exclusive For instructions on changing the current state see section 4 7 above
93. lowing you to add to or remove from the collection of selected nodes To select a link click right on it It will become drawn in hilited outline form Once again if the shift key is held down while clicking it will reverse the selection status of only the link being clicked on which can be used to add or remove from your collection of selected links Links cannot be selected by dragging the selection rectangle over them Nodes and links cannot both 290 be selected at the same time so whenever you select links any nodes that are selected will become unselected and vice versa 3 6 Moving Nodes and AutoGrid To move a node click down on it drag it to its new position and then release the mouse button If you wish to move a set of nodes and the links between them select the nodes you wish to move then click down on one of them and drag the set to the new desired location There is an underlying grid of positions and when you add a node or move a node the node will be shifted slightly so that its center is directly over one of these grid positions providing the autogrid is turned on This allows you to quickly draw a network whose nodes are perfectly aligned and with some links running perfectly horizontal or perfectly vertical The autogrid is turned on when there is a check mark in front of the Layout AutoGrid menu entry To turn it off or on choose the Layout AutoGrid menu entry If you want to change the sp
94. ly on the order in which they are reversed Unless you know a good order to do the reversals you should reverse them all at once rather than one by one so that Netica can choose a good order to do them 61 8 2 Node Absorption Node absorption is the process of removing nodes from a belief network or decision network and making any necessary adjustments to the resulting network so that any inference done with it yields the same results as before the nodes were removed except of course you can t interact with the removed nodes The local representation is changed but the global relationships are not changed In probability theory this is sometimes loosely called summing out a variable It leaves the full joint probability distribution of the remaining nodes unchanged As an example suppose you have a large network 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 will be of interest In every query of the new application a particular 4 of these 10 will always have the same findings For example one of the nodes in the original network might by Gender and in the restricted application the network will only be used for females so you would like to enter a perma
95. malize menu command 49 Relation Randomize menu command 49 Relation Remove menu command 49 relationship of node 43 Relation Uniform Probabilities menu command 49 Relation View Edit menu command 43 Remove Findings tool button 22 removing link bends 30 removing Netica 8 removing node relationship 49 removing states from node 38 requirements system 8 reshaping a link 30 resizing relation dialog box 46 resizing nodes 78 retracting findings 22 retrieving a case 65 reversing a link 60 running Netica 8 Russell amp N95 17 84 sampling 68 saving a case 65 saving compiled network 22 saving network to file 31 scenario 26 screen dump 81 scrolling multi purpose box 39 network window 34 node description 39 relation dialog box 46 second order probabilities 73 selecting cells of relation dialog box 48 selecting nodes and links 29 sequential decisions 54 Shachter s algorithms 64 Shachter86 84 Shachter88 84 Shachter89 84 shift key 29 relation dialog box 48 size of nodes 78 Smith amp HM93 84 solving decision networks 53 space at node border 36 Spiegelhalter amp DLC93 16 84 spreadsheet program copying to from 48 66 state name 38 67 state names other 79 State Value edit box of node dialog box 39 state values of node 39 States edit box of node dialog box 38 states of node 38 40 statistics 17 structure learning 70 Style menu 77 style of display 77 Style Font submenu 78 Sty
96. me in the new network the titles of the nodes are ignored The state names of the nodes if present should also be the same Any findings not corresponding to a node in the new network will simply be ignored All name comparisons are case sensitive Real number values that you have entered as findings for discretized continuous nodes are saved in case files rather than just the state they correspond to This enables reading the case into another network whose node for that variable has been discretized in a different way perhaps finer or courser If you read in a case and the case file has a value that isn t any of the states of the corresponding node in the network then an error messsage will be displayed For example if node color has the states red and green and in the case file the value for color is blue the message will be displayed An exception to this occurs if one of the states of the network node is named other Then the case will be read without error and the finding for the node will be other To remove the current case from a belief net you can use the Network Remove Findings menu command with no nodes selected It will leave the network with no findings entered and if it is an auto update network then its beliefs will be updated to reflect that If some nodes are selected when you do the Remove Findings command then only the findings for those nodes will be retracted 9 1 Multi Case
97. ms Chapter 2 discussed using belief networks for probabilistic inference Belief networks are used to determine new beliefs in the form of probabilities as observations are made or facts are gathered They are composed only of nature nodes To form a decision network also known as an influence diagram you add decision nodes and utility nodes also known as value nodes Decision nodes which are traditionally drawn as rectangular boxes correspond to variables or events that you will be able to control Utility nodes are drawn with a diamond or flattened hexagon shape and correspond to quantities you want to maximize The decision network as a whole represents a planning problem that you face or that some other agent often called the decision maker faces Netica can find values for the decision nodes that will result in the largest possible expected value for the utility node or sum of them if there is more than one This is known as solving the decision network Once the network is solved you or the decision maker can begin to enact the plan by taking the prescribed action for each decision as it arises Links that go into a decision node have a special meaning and are called informational links They indicate what will be known at the time the decision is to be made That is the decision maker will know the values of all the nodes which have links into that decision node and will not know the values of any other nodes
98. n networks policy iteration etc within the overall context of intelligent agents and AI software 17 2 Probabilistic Inference 2 1 Belief Networks and Probabilistic Inference A belief network also known as a Bayesian network or probabilistic causal network captures believed relations which may be uncertain stochastic or imprecise between a set of variables which 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 A classic example of the use of belief networks 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 unmeasurable disease variables 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 network and provide the initial relations between variables often in the form of conditional probabilities based on his medical training and experience with previous cases Then the network probabilities may be fine tuned by using statistics from previous cases and from new cases as they arrive When the belief network is constructed one node i
99. n a very fine scale corresponding to the number of electrons on a capacitor You only need consider the scale of interest when setting whether a node is continuous or discrete It is common to have a continuous variable that you want to break up into ranges so that you can treat it as a discrete variable which is known as discretizing the variable It is usually best to make it a continuous node and then discretize it with a range list as described below in section 4 8 Node State Range rather than just making it a discrete node This provides better documentation of the node and makes it easier if at a later time you want to discretize it another way i e with a different number of states or different cutoff points for the state ranges A utility node must always be made continuous and a decision node must always be made discrete 4 6 Node Kind Directly below the name entry area the node dialog box has a selector which may be used to turn the node into a nature node decision node or utility node also known as a value node Nature nodes are sometimes called deterministic nodes when they depend on their parents in a deterministic way or chance nodes when the dependence is probabilistic When a network is composed entirely of nature nodes it is called a belief network also known as a Bayesian network If it also has decision and utility nodes it is called a decision network also known as an influence diagram Deci
100. n state These decisions are the ones that maximize the expected value of the sum of the utility nodes After you do an Optimize Decisions command and Netica has finished optimizing it will pop up a node relation dialog showing the decision functions for the first decision node In general you can use the node selector in the upper left to see the decision functions for other nodes For the umbrella example the decision will be forecast best decision sunny dont_take_umbrella cloudy dont_take_umbrella rainy take_umbrella Decision networks can also be solved using node absorption which is discussed in section 8 3 Select all the nodes and then click on the absorb tool bar button The network will be decomposed and only the decision nodes and utility node will be left Each decision node will have the optimal decision as its relation but it may have some parent links removed Any removed links are ones that are irrelevant to the decision All the utility node s parents will be removed and it will have the maximized expected value as its relation After observing the relations and perhaps copying and pasting them to a new network you can restore the original network with an Edit gt Undo menu command If you wish to see an example of a slightly more complicated decision network with 2 sequential decision nodes open Car_Buyer_Neapolitan in the Examples folder It is described in Neapolitan90 and is based on the classic Car Buy
101. nent finding of female for the Gender node These nodes are called context 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 out of 10 The nodes that will always have new findings are called evidence nodes and those whose beliefs you may want are called query nodes The hundreds of other nodes might be involved in intermediate calculations but you don t care about their values explicitly You can simplify the large network down to one with just 6 nodes using a process called node absorption In this process nodes are removed from the network but the links and probability tables of the remaining nodes are adjusted in such a way that any probabilistic inference done with the remaining nodes will yield exactly the same results as if the absorbed nodes were present Node absorption can simplify a network considerably since nodes are being removed but in some cases it can make the network more complex because extra links are added Here is how you would reduce the large network First enter the permanent findings for the context nodes in the usual way of entering findings as described in section 2 5 Then select all the nodes to be absorbed i e all the nodes except the evidence and query nodes and click on the absorb tool button which is the tool bar button with the five pointed star or do a Network Absorb Nodes menu command The selected node
102. ng Started 6 1 1 Netica AppliCatIOD n eene eate te oe rea Ue ae ta bo Tee eh eor ee rasa doe eee 6 1 2 T stalIatYORscos sede teu Satu ate e t undae ni edes e EA 8 1 3 Menu Commands and Tool Bar eene 8 1 4 Quick T te E 9 1 4 1 ProbabilisticInference ec edit teasntvadacadstedoed duct aswenaaeds 9 1 4 2 Network Construction and Transformation 11 E43 ACASE PUES erneit tud eee ap du 13 1 4 4 Decision Problems eeeeeeeeeeeeeeeeneeenne 14 1 4 5 Equations and Time Expansions eene 15 1 5 Introductory References for Belief and Decision Networks 16 2 Probabilistic Inference 18 2 1 Belief Networks and Probabilistic Inference 18 2 2 Netica s Probabilistic Inference eseeeeeee 19 2 Example Bele E NetWork AS dso leur rad eI REOR hide 20 2 4 Compiling a Belief NetwOEK o ege n Editer dpa de aere ae 21 2 5 Entering and Retracting Findings eene 22 2 6 Belief Updating and AutoUpdating esee 23 2 7 Negative and Likelihood Findings eeeeeeee 23 2 S COBSISEEHOY ou ncc Mum e Ue dde toned vm pcm D er soa 24 2 9 Most Probable Explanation 4 eec eeee cette eren eene een nen 25 3 Constructing Belief and Decision Networks 27 3 1 Opening a WAO a A Gui a i 2T 3 2 Adding NOS eo tei ded cies a a teas e a
103. ng and inference using them 9 2 Case File Format Case files single case or multi case are pure ASCII text files They must contain CASE 1 somewhere in the first 3 lines 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 its state number preceded by a character the first state is 0 Using the state names is preferred since the order of the states may be changed some time and that would render a file with state numbers invalid The value of a continuous variable is given by a number in integer decimal or scientific notation e g 3 21e 7 If it has been discretized then the value may be given by a state name or state number instead but the continuous number is preferred if it is available That way the case file can be used for
104. nks from more immutable to less immutable variables You could learn its probabilities as described in chapter 10 from a set of cases consisting of the forecast and what the weather turned out to be Then you could put it in a library to later graft into networks for inference involving the weather and its forecast such as the decision problem discussed in chapter 6 Weather instrument_status flow_rate x2 x1 temperature x3 Figure 7 1 Example of a tiny network library instrument As another example suppose you have a device for measuring the flow rate in a pipe It produces biased readings depending on the ambient temperature and it can malfunction in a few different ways each of them producing wrong or inaccurate readings You can model the device 56 with a 4 node network consisting of one node for the reading on the device and 3 parent nodes corresponding to actual flow rate ambient temperature and device 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 The rightmost node in diagram 6 1 shows how it will appear A section below describes in more detail how to do this Later if you have a network to model a situation in which you use the instrument to make two measurements of the flows in two connected pipes located in the same room you just duplicate the device characteristics node from th
105. nt has lung cancer from 5 5 to 48 9 but then indicating that the patient has made a visit to Asia decreases that belief to 37 1 because the abnormal XRay is partially explained away by a greater chance of Tuberculosis which the patient could catch in Asia If you choose Unknown from the findings pop up menu then any finding for that node will be retracted and if you choose Likelihood you will be queried for the probabilities of an uncertain finding virtual evidence for the node You can also click directly on the name of the finding a second time to retract the finding or hold down the shift key while clicking on the name of the finding to enter a negative finding Each time you enter a finding or retract one the beliefs at all the nodes will immediately by updated to account for the new information If you wish updating to only occur when you do a Network Update command you can turn off the auto update feature of the network by choosing Network Automatic Updating from the menu the menu item will be checked only when auto updating is on If you want to observe or change the conditional probabilities of a node which express its relation with its parent nodes select the node by clicking once on it and then do a Relation View Edit command or click on the tool bar button with the green inverted V s A special window called the relation dialog box will open which displays the probabilities in a table The left
106. o be given a title which has no such restrictions On the displayed network each node can be labeled with its name its title or both together separated by a colon or parenthesis To display all the nodes by name choose Name from the Style Node submenu to display them by title choose Title or to display them using both choose Name Title or Title Name The choice that you make will apply to all the nodes of the network If you are displaying nodes by title and some nodes don t have a title then their name will be used instead The starting style of a new network is Title but you might not notice this if you don t use titles since then just the node names will appear zT 11 2 Font and Size If you wish to determine or change the font used for the writing within nodes select some nodes and then click Style Font A dialog box will appear showing the current font and its size and will allow you to change them The choice that you make will apply to all the nodes of the network Whenever you choose a new font or a new font size all the nodes will be resized so that the writing within them fits nicely In fact the way you enlarge or shrink the nodes of a network is to choose a larger or smaller font size If a link is selected when you click Style Font then the new font and size will not apply to the nodes of the network so no resizing will be done but rather to the labels of all disconnected links 11 3 Node Styles Th
107. o paste in the names of all the states at once which you have copied from another node or even from another program You simply enter the names of all the states into the box separated by space s tabs commas or on separate lines If the number of states in the list is different from the node s current number of states the node s number of states will be changed 40 An example entry is low medium high 4 10 6 Node Ranges When a node dialog box s multi purpose selector is set to Ranges you can enter or view the discretization of a continuous variable or supply a number for each state of a discrete variable You can also do these operations using the Range setting boxes described earlier which have the same capabilities and effect see sections 4 8 and 4 9 above However usually this method is more convenient especially if you to enter many evenly spaced values or if you want to paste in the ranges of all the states at once which you have copied from another node or even from another program You simply enter all the range levels into the box separated by space s tabs commas or on separate lines See section 4 8 Node State Range above for a description of the meanings of these numbers If the node is continuous then there should be one more number than the desired number of states and if the node is discrete then there should be one number for each desired state If the number of states implied by the list is d
108. ode Belief Bars 78 Each node will be displayed as a box labeled at the top with the node s name title or both depending on what was chosen using the Style Node submenu The name of each state is shown in a section to the left along with a number expressing the belief probability of that state as a percentage If the name is too long to fit it will end with an ellipsis If the percentage is too small to display numerically but nonzero then it will be displayed as 0 In a section to the right are bar graphs depicting the belief levels Vertical dotted lines mark the 0 25 0 5 and 0 75 levels If the belief in one state is certainty due to a finding for this node then its bar will be bordered above and below by black lines If the current belief percentages and positions of the bars are invalid for the findings entered probably because the latest findings haven t been taken into account yet the bars will be drawn in a fuzzy dotted manner PC Neighborhood A park is constructed Blood Pressure False True KinkedTube Figure 11 1 Example of nodes displayed in different styles Upper left is Labeled box Name Title style lower left is Belief Bar style lower right is Belief Meter style and upper right are a few different kinds of nodes in Labeled box Name style 11 3 2 Belief Meter Belief meters are often the display of choice for binary variables like true false propositions or okay faulty condi
109. ode 36 Car Buyer example 54 case 65 identification number 68 transferring networks 66 case file 65 comments 67 creating 66 creating by sampling 68 example 68 format 67 learning from 72 CASE 1 file format 67 causal network 18 cell of relation dialog box 44 chance node 37 chance node tool 27 37 characters overlapping 81 Charniak91 16 83 checking probabilistic relation 49 child node 18 Circle node style 78 classification 70 Clipboard Viewer 81 clique tree 19 Close button in node dialog box 36 in relation dialog box 46 closing relation dialog box 46 compile network tool button 21 compiling belief network 21 computation costs 53 conditional plan 51 configurations of parents 44 consistent findings 24 constructing decision networks 52 network libraries 58 networks 27 Cont Discrete selector of node dialog 36 context node 62 contingent plan 51 continuous value findings 66 continuous vs discrete 36 co operating agents 53 copying pasting graphics 80 copying nodes 33 copyright notice 2 current state of node dialog box 38 customizing for end user 77 80 cutting and pasting in relation dialog box 48 cutting nodes 33 database of cases 66 date published 2 Dean amp W91 83 decision function 51 decision network 51 constructing 52 solving 53 solving by node absorption 64 decision node 37 51 decision node tool 27 37 52 default node style 78 degree of fading 76
110. om one node to another first click on the link tool bar button it is the one with the arrow pointing down not the up facing pointer do a Modify Add Link command or press F12 When you next move the cursor to the active window it will change to a link shape indicating that it is ready to add a link Click on the node that you wish to be the parent and then click on the child node Alternately you can click down on the parent and while holding the mouse button down move to the child and then release it The link will appear A later section will explain how you can change the shape of a link To add a series of links double click on the link button or double press the F12 button The cursor will change to a link shape as before but now it will stay that way as you add multiple links To exit this link adding mode click again on the link adding button or press the F12 key again or click on the pointer button or click on a node adding button or press a node adding key 228 3 4 Undoing and Redoing While building or changing the network you can undo the last operation by choosing Edit Undo from the menu or pressing Ctrl Z To undo operations previous to that one repeatedly invoke Edit Undo or repeatedly press Ctrl Z After a series of undos you can redo one or more of them by repeatedly invoking Edit Redo or pressing Ctrl Shift Z Netica will save a certain number of the previous steps for undoing at least 4
111. om which you can select the case file After you press Okay any existing findings in the network will be removed the file will be read and the findings entered into the network If some nodes are selected then Netica only removes findings and reads new ones for the selected nodes it also beeps and puts a notice in the Messages window that the whole case wasn t read If the network is auto updating then belief updating will be done automatically to account for the findings of the case Continuing with the medical example started earlier a case might correspond to a certain patient When you want to work with a new patient you save all the information gathered for the first patient into a case file before removing it from the network perhaps using the patient s name as a file name When it comes time to reconsider the first patient perhaps some lab results have arrived you just read that person s case file 65 For another example each case could be a political riding The findings would be details about that riding such as demographics poll statistics etc and the belief network could be used to predict the percentage of votes each political party will get in the next election As new information about a riding arrived its case file would be kept updated It is possible to read a case into a different network than the one it was originally saved from Findings from nodes of the old network will be entered into nodes of the same na
112. ometimes link reversals can be used to search for more simple networks given a network that was originally learned from data In that case Netica might not always automatically remove links that should be removed because although these links will be weak they will not be completely ineffectual perhaps because the probability tables learned are not exact Links are termed weak when their removal has little effect on the full joint probability distribution and therefore little effect on inference results see Boerlage94 You would have to remove these weak links by hand To reverse a link you select it and then do Modify Reverse Links or click on the link reversal button which is the tool bar button with two arrows pointing in opposite directions If a node is selected when you click on the link reversal button it will do all the link reversals necessary to make all links involving the node point to it unless the node has a finding in which case they will all be made to point away from the node If all links are made to point away from the node then many extra links may have to be added between the ancestors of the node not just its Markov boundary and Netica may report that there is not enough memory available If you have several links to reverse you can select them all e g by shift clicking on them and then click on the link reversal tool bar button The amount of time and memory required to reverse a set of links depends great
113. ompile a belief network first make sure it is the active window i e the one in front with the darkened title bar If it isn t you can make it active by clicking on an exposed part of it or choosing its title from the Windows menu Then do a Network Compile menu command or click on the lightening bolt tool bar button The appropriate data structures for fast inference will be built internally The default display style for the nodes will be changed to belief bar so if the nodes haven t had their display styles set see chapter 11 Display Style and Printing then they will be displayed in belief bar style If you compile Asia you will see something like the following Visit To Asia Smoking Visit 1 01 Smoker 50 0 No Visit 99 0 NonSmoker 50 0 Lung Cancer Bronchitis Tuberculosis Present 1 04 Present 5 50 Present 45 0 Absent 99 0 Absent 94 5 Absent 55 0 Tuberculosis or Cancer True 6488 False 93 5 MN XRay Result Dyspnea Abnormal 11 0 M i Present 43 6 NE Normal 89 0 Absent 56 4 Each state is shown with its belief level probability expressed as a percentage and as a bar graph see chapter 11 for more details For small networks the Compile command will seem to perform instantly For large networks it may take a few seconds in which case the progress will be displayed in the Messages windo
114. on for the desired kind while holding down the Ctrl key 52 You do not have to enter a relationship for decision nodes since that is what is found when the decision network is solved Utility nodes should always be made continuous and do not need to be discretized Also there must be only one utility node in this version but not the forthcoming version of Netica and it must not have any children 6 2 No Forgetting Links Normally when a decision maker makes a later decision he will know at least everything he did when he made earlier decisions Also he will know what earlier decisions he made That is represented in the decision network by ensuring that the decisions are in a sequence with a link from one to the next and that each decision node later in the sequence has links to it from all the decisions earlier and from all the parent nodes of earlier decisions These links are called no forgetting links since they indicate that all the information that was available earlier is still available to the decision maker Not considering computation costs having more information to make decisions always leads to a policy having greater or equal expected utility So to find the best policy it is important to have no forgetting links After you have constructed a network you can make sure it has all the required no forgetting links by doing a Network Add No Forgetting Links menu command Make sure you have added links so that
115. ons for more details 4 10 3 Input Name When the multi purpose selector of a node dialog box is set to Input Name you can view or enter a name for each of the links going to the node As soon as you set the selector to Input Name an additional selector will appear to the right of it Each choice of the new selector will correspond to a link and will be labeled with the current link name if the link has one in parenthesis and or the name of the parent node it comes from if the link is not disconnected See chapters 7 Network Libraries and 12 Equations for the purpose of link names 4 10 4 Link Delay When the multi purpose selector of a node dialog box is set to Link Delay you can view or enter a time delay for each of the links going to the node As soon as you set the selector to Link Delay an additional selector will appear to the right of it Each choice of the new selector will correspond to a link and will be labeled with the link name if there is one and or the name of the parent node it comes from if the link is not disconnected 4 10 5 Node States When a node dialog box s multi purpose selector is set to States you can enter or view how many states the node has and what their names are You can also do these operations using the State Name setting box described earlier which has the same capabilities and effect However sometimes you may find this method more convenient especially if you want t
116. ormation between the Messages window and any text file When you are finished with your Netica session you can end it by doing a File Exit menu command If you have created or changed some work without saving it Netica will ask if you want to save it before terminating 1 4 1 Probabilistic Inference First we will read a belief network stored on disk Do a File Open menu command and when the standard file opening dialog box appears use it to open the file called Asia in the folder Examples A window will appear containing a belief network consisting of several connected nodes This network is a classic very simplified example network for diagnosing patients arriving at a clinic You can prepare the network for inference with a Network Compile menu command or by clicking on the lightening bolt tool bar button When the compilation is complete the default display style changes so that nodes are displayed with bar graphs showing the beliefs for each of their states You can enter a finding also known as an observation or evidence for a node by clicking on the name of the finding to the left of the bar graph You can also enter a finding by right clicking on the node and choosing it from the pop up menu that appears When the finding is entered the displays of all the nodes will be adjusted to account for it For instance 9 putting an abnormal finding for XRay Result node increases the belief that the patie
117. pdating So if the network is kept valid by belief updating after each finding is entered see auto updating then you will be alerted as soon as you try to enter an inconsistent finding otherwise you won t be alerted until the next belief updating is in progress 2 9 Most Probable Explanation Given findings for some nodes you may want to find the most probable configuration of values for the rest of the nodes This can be thought of as providing a plausible explanation for the observed findings and is called the most probable explanation or MPE Notice that you cannot determine the MPE simply by taking for each node the state with highest belief after regular belief updating which finds the marginal posterior probability for each node For example in a lottery for which we know there is one winner it might be most probable for each individual person to lose but then the overall configuration would have everybody loosing which contradicts the one winner evidence Finding the MPE would select one representative person to win and the rest would be losers Netica can be used to find the MPE To indicate that you wish to do MPE updating for a network instead of regular belief updating make sure the network is the active window and choose the Network Most Probable Expl menu item The menu item will then have a check mark beside it indicating MPE updating will be done by choosing it again you can toggle the check mark off You will have
118. population as the cases used for learning Typically the values for some variables of the new case will be known These are entered as findings and then probabilistic inference is done 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 query nodes If the links of the network correspond to a causal structure and the query nodes are ancestors of the nodes with findings then you could say that the network has learned to do diagnosis If the query nodes are descendants then the network has learned to do prediction and if the query node corresponds to a class variable then the network has learned to do classification Of course the same network could do all three even at the same time The belief network learning task has traditionally been divided into two parts 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 network Parameter learning determines the conditional probability relationship 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 While learning Netica assumes independence between each of the cond
119. pter 10 Learning from Cases 2 2 Netica s Probabilistic Inference Netica uses the fastest known algorithm for exact general probabilistic inference in a compiled belief network which is message passing in a join tree or junction tree of cliques The algorithms used are described in SpiegelhalterDLC93 and Neapolitan90 In this process Netica first compiles the belief network into a join tree The join tree is implemented as a large set of data structures connected up with the original belief network but invisible to you as a user of Netica You enter findings for one or more nodes of the original belief network and then when you want to know the resultant beliefs for some of the other 19 nodes belief updating is done by a message passing algorithm operating on the underlying join tree It determines the resultant beliefs for each of the nodes of the original belief network which it displays as a bar graph or a needle meter at each node 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 Netica can also do probabilistic inference by link reversals and node absorption For most applications you will want to use the compiled join trees because usually they are much faster and don t destroy the existing network but you may want to use node absorptions when yo
120. re that forms at its non arrow end and dragging it away from the parent node or by selecting the link and doing Modify Disconnect Links To reconnect the link to a new node drag the non arrow end over the new parent and release the mouse button Disconnection reconnection is useful to change the links of a network without loosing the conditional probability relations of the nodes Remember that to just delete a link you simply select it and then press the lt delete gt key You can cut and paste nodes and subnetworks within a window or between windows Try opening a network such as Car Diagnosis 0 select part of it press Ctrl C to copy it to the clipboard Ctrl N to create a new network click in the middle of the new window to indicate where to put it and then Ctrl V to paste it into the new network You can cut and paste other parts of the network or other networks add nodes etc and then connect up the disconnected links as described in the previous paragraph In this way you can take knowledge from previous applications perhaps save it in a network library and re use it to construct a new network for a new application Of course at any point you can do a File Save command to save the current version of the network to file overwriting the previous one or a File gt Save As command to save it to a new file You can change the characteristics of a node by using a node dialog box which is obtained by double
121. s Main Fuse Battery Age Voltage at Plug and Spark Plugs and then click on the star tool bar button or do a Modify Absorb Nodes command The selected nodes will be absorbed links will be added and removed and probability tables adjusted to maintain the global relationship Now do Network gt Compile and observe the belief is 1 47 that Spark Quality is good as it was before the absorption If you then do Network Remove Findings the belief changes to 25 496 which is what it was in the old network before any findings were entered Link reversal changes the direction of a link without effecting the overall global relationship of the rest of the nodes i e the joint probability distribution Select a link and then click on the double arrow tool bar button or do a Modify Reverse Links command Netica may have to add extra links in order to maintain the joint probability distribution or it may be able to remove some links To change the display style of some nodes first select them and then make a choice from the Style Node submenu For the Asia network the most useful displays are belief bar or belief meter although if you were creating a network for an end user you may want to hide a node like TbOrCa because it is not of interest so you would give it a style of Hidden If you want to hide all the links you can use Style Net Hide Links The Style gt Font and Style Size submenus may be used to chan
122. s are not met Netica will not produce an erroneous result but will just absorb as many of the nodes as it can and then display a message explaining why it was impossible to proceed 64 9 Cases and Case Files The set of all findings entered into the nodes of a single belief network is referred to as a case A case usually provides some information about a particular object person event etc It may be transferred from the belief network to a file for later retrieval Perhaps you want to work with a different case but you need to be able to restore the original case to the network later on in order to enter new findings recently obtained or to make further queries To save to file all the positive findings from the belief network in the active window make sure no nodes are selected and then do a File Save Case As menu command You will be presented with the standard dialog box to choose the file name After you enter it and press Okay all the positive findings will be saved to that file If some nodes are selected then only the findings for the selected nodes will be saved and Netica will beep and put a notice in the Messages window If you later want to read the case back in to its original belief network you first make sure that the original belief network is the active window and no nodes are selected and then do a File Get Case menu command You will then be presented with the standard dialog box for choosing a file fr
123. s itecto NR 8 2 Node ABSORP DEON yee eet it ot DER R D Ee SEU ONIS dba NN 8 3 Probabilistic Inference by Node Absorption ssss 9 Cases and Case Files 9 4 Multi Case Elles narret eee oce eee ene roe eene ers des 9 2 Case Pile Format ie ned cents eiay eee nen 9 3 Generating Random Cases iccisssssseccssunscesssaveeaceesaseeesansconanedesuneeoaeies 10 Learning from Cases IO T HOW TODO Wied hedge ee te ees ies Chet opis 10 1 1 Single Case Learning eese 10 1 2 Learning From a Case File ettet 10 2 Experience ninin sie Oa eve ue rae yeu bea e Qe bela POM NO URS 10 5 Bayesian Learmint iusso en sd Lans od bte aio 104 SACS cele ss DU ts adsense Ios 11 Display Style and Printing 11 1 Node Name and Tithe Display eontra ees llc Boni AU S078 oc esos to edt e pita eiue bie gasses IUE IB Enn Ig m ZI Belef Bats sse Dre Gngn a sips dae etait 11 3 2 Belef M t t seien edit tread T EROR ERR ITA NetStyleSa uocat I EDS UI COO IR RANT UI ARR a 11 5 Copying and Pasting Graphics eene 1 150 Pinuna S eoe tro Bueno repr ibn Itn N cn bcn iocis ap 12 Equations 13 Bibliography 14 Index 1 Getting Started Welcome to the Netica Application from Norsys Netica is a versatile fast user friendly program that you can use to find patterns in data create diagrams encoding knowledge or representing decision problems use these to answer queries and find optimal dec
124. s of parent values On the right hand side is one column for each state of C The numbers in the table provide conditional probabilities for the values of C given that the parents take on the configuration of their row For example the 10 000 percent in the upper left corner means that P C Small A Low B True 0 1 The number 3 2e 12 at the bottom right means P C Large A High B False 3 2 x 10 14 The two empty cells on the third row indicate probabilities that have not yet been specified and the three x s on the fifth row indicate that the designer believes that the condition A High while B True is impossible 5 3 Changing Table Entries You will often bring up a relation dialog box just to view the relation it represents For example if you have just solved a decision network you can use it to view the optimal decision functions that Netica has found However its main purpose is to enter or change node relations when building a belief or decision network or doing what if analysis with an existing network If the dialog is for a deterministic node then you can change a table entry also known as a cell of the table simply by clicking down on top of it and then making a choice from the pop up menu which appears 44 If the dialog is for a chance node then you can change a probability by clicking on it to select it and then typing in the new number Or you can click on it to select it then click within the selection where
125. s used for each scalar variable which may be discrete continuous or proposititional true false Because of this the words node and variable are used interchangeably throughout this document but variable usually refers to the real world or the original problem while node usually refers to its representation within the belief network The nodes are then connected up with directed links If there is a link from node A to node B then node A is sometimes called the parent and node B the child of course B could be the parent of another node Usually a link from node A to node B 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 18 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 Neapolitan90 or Pearl88 However most people seem to intuitively grasp the notion of links and use them effectively without concentrating on the precise definition Finally probabilistic relations are provided for each node which express the probabilities of that node taking on each of its values conditioned on the values of its parent nodes Some nodes may have a deterministic relation which means that the value of the node is given as a direct function of the parent node values After the belief network is construc
126. s will be removed and some links may be added and or reversed 62 If you want you can absorb the nodes a few at a time by selecting each group and clicking on the absorb tool button The final result of absorbing a set of nodes is not dependent on the order in which they are absorbed but the time and memory required to do the absorbing may be greatly affected If you have a set of nodes to absorb and you don t know a good order to absorb them then it is best to absorb them all at once so that Netica can pick a good order Returning to the example the resulting 6 node network 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 evidence node then you can then further simplify things by removing any links that go from evidence node P to evidence node C providing C does not have a query node as a parent This means that if you can reverse links as described in the previous section to make all the evidence nodes ancestors of all the query nodes then you can remove all the links between the evidence nodes Any evidence node that is left completely disconnected by this operation is irrelevant to the query and can be deleted And now you can examine the conditional probability relations of the query nodes to see directly how they depend on the findings You may just be able to look up the desired probabilities without do
127. servation 24 impossible conditions 47 inconsistent findings 24 independent findings 24 influence diagram 51 informational link 51 input names of node 40 installing Netica 8 Instrument example 56 58 introduction to BNs references 16 irrelevent informational links 54 iterated policy making 54 join tree 19 junction tree 19 keys arrow 30 31 45 delete 32 end 34 46 enter 28 35 home 34 46 page down 34 46 page up 34 46 shift 29 kind of node 37 Kind selector of node dialog box 37 knife tool bar button 57 Labeled box node style 78 large network diagrams 81 Lauritzen amp S88 83 Layout AutoGrid menu command 30 31 Layout Drawing Size menu command 34 Layout Grid Spacing menu command 30 31 Layout Show Page Breaks menu command 81 learning 87 belief networks 70 degree 71 fading 75 forgetting 75 from case file 72 from cases 70 from single case 71 parameter 70 structure 70 unlearning 71 legal disclaimer 2 8 libraries belief network 56 LicAgree txt file 8 license agreement 8 license password 8 likelihood finding 24 link 18 adding 28 deleting 32 disconnecting 32 57 hiding 80 informational 51 name 32 40 style 78 reconnecting 33 58 removing bends 30 reshaping 30 link delay 40 link reversal 60 links added removed 60 order of 61 link reversing tool 61 living document 55 Load button in node dialog box 35 in relation dialog box 45 magnif
128. sion nodes represent variables that the decision maker can control and utility nodes represent variables the decision maker is trying to optimize See chapter 6 Decision Problems for more information You can also change node kinds straight from the network window without using a node dialog box To do this select a node or set of nodes you wish to change and while holding down the ROT Ctrl gt key click on the tool bar button indicating the kind of node you wish them to become To convert them to nature nodes click on the yellow oval to convert them to decision nodes click on the blue rectangle and for utility node click on the green hexagon 4 7 Node States In the node dialog box next to the label States is a down arrow which yields a pop up menu of the node s states By choosing a state from the menu that state becomes the current state of the node dialog box Its name will appear in the text edit box to the right of the pop up menu allowing you to change the name It is not necessary that the states of a node have names but if one state is named then they all must be It is highly recommended that a discrete node be given state names for clarity and documentation purposes although it is not as necessary for discretized continuous nodes When you enter a new state name Netica will check that it meets the restrictions of an IDname It must start with a simple letter a z or A Z it must be composed only of simple
129. t appear on the tool bar when you first start Netica Simply double click on a blank area of the toolbar or choose Window Customize Toolbar and use the resulting dialog box to add any desired buttons Once they are on the tool bar buttons can be rearranged or removed by holding down the Alt key while dragging them 1 4 Quick Tour All you need to know to complete this tour is how to use a Windows computer You do not need knowledge of belief networks decision networks or Netica although you may not fully understand what is happening until you have that knowledge and have read other chapters in this guide First make sure you have completed the above described installation You should duplicate the Examples folder in case you accidentally change some of the supplied files Then run Netica by double clicking on its icon The first time you run Netica it will ask you for a password Enter the license password from your invoice or click on the Reduced Mode button if you don t have one The workspace window will open and in its lower left corner there will be an icon for a minimized window called Netica Messages Usually when you try to do an operation that Netica can t perform it will display a dialog box telling you However for some minor operations like clicking in the wrong place Netica will just beep In that case you can look in the Netica Messages window and there will be an explanation You can copy and paste inf
130. t of course findings can t be entered for removed nodes and their resulting beliefs are unavailable Some reasons to do these transforms are to simplify the network apply the network to more specific problems gain understanding of the network or of the real world relations or put the network in a form for easier probability or function assessment 8 1 Link Reversals Suppose P and C are discrete or discretized nodes within a network and that P is a parent of C Since there is a link going from node P to node C the relation between the two nodes is expressed as probabilities for the states of C conditioned on the state values of P or a function providing C s value in terms of P s value if the node is deterministic But sometimes you might want to know what the probabilities for the states of P are conditioned on state values of C In order to do this you reverse the link from P to C When that link is reversed the other links and the probability tables of the child and parent nodes are adjusted in such a way that any probabilistic inference done after the reversal will yield exactly the same results as before the reversal In other words the full joint probability distribution of the network does not change when a link is reversed The global relationship between the nodes remains the same just the local expressions of it have been changed It is a probabilistic generalization of function inversion During the reversal links may
131. t to never having entered it even if there were other findings entered in between Another way of retracting the findings for some nodes is to select them see Selecting Nodes and Links and then do a Network Remove Findings menu command or click on the tool bar button with a red cross over the case symbol yellow rectangle with black dot lines If you wish to retract all the findings entered for all the nodes in the network make sure all or none of them are selected and then do a Network gt 22 Remove Findings menu command This is useful if you are finished with one case and wish to move on to another 2 6 Belief Updating and AutoUpdating If you have been experimenting with entering findings into the Asia belief network you will have noticed that belief updating is performed immediately after entering each finding resulting in a new setting of belief bars for each node in the network That is fine for a small network like Asia since the belief updating occurs very quickly For a large network the belief updating will take longer so you may want the ability to enter findings for many of the nodes and then have it do the belief updating Belief updating is done immediately after entering a finding only if auto updating is turned on for that network It is on if the Network Automatic Updating menu entry is checked when the network is the active window You can turn it on or off by choosing Network gt Automatic
132. ted it may be applied to a particular case 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 6 hot 0 3 indicating the subjective probabilities that the temperature is cold medium or hot The final beliefs are sometimes called posterior probabilities with prior probabilities being the probabilities before any findings were entered Probabilistic inference done using a belief network is called belief updating If we want to apply the network to a different case then all the findings can be retracted new findings entered and belief updating repeated to find new beliefs for all the nodes Probabilistic inference only results in a set of beliefs at each node it does not change the network 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 cha
133. there is a path running through all the decision nodes to fix their sequence in time before doing the command There are a couple of reasons why you might not want all the no forgetting links included With them the decision tables of the last nodes may become gigantic requiring a great deal of computation time and memory In such a case it is useful to be able to forget some items especially if the decrease in expected utility is small or none The other reason you may not want all the no forgetting links is that you may be trying to model a decision situation where you have two or more co operating decision makers who are forming a policy together but who won t be able to communicate when the decisions are to be made Netica currently requires all the no forgetting links to be included in a decision network before it can solve it but the next version won t it will operate on the theory explained in Zhang amp QP94 6 3 Solving a Decision Network Once the network is built you can solve it using the Network Optimize Decisions menu command It will attach to each decision node a deterministic function the optimal relationship is always deterministic This function provides a value for the decision node for each possible configuration of parent values Since the links into a decision node indicate what the decision M re maker will know when he is about to make the decision this function provides a decision for each possible informatio
134. ties 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 These are sometimes called second order probabilities but in this example they are really just a probability distribution over possible ratios If you discretized the possible ratios then it would be easy to set up a belief network 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 would become too complicated Instead Netica uses the concept of experience which is a measure of the number of cases relating to some situation that Netica has seen 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 value corresponds closely to the number of cases that have been seen normally it is 1 more than the number of cases or its equivalent This form of experience has sometimes been called the equivalent sample size or ess To save space Netica doesn t store experience US numbers for nodes that haven t been involved in any learning and haven t had a manual entry of experience Before learning begins providing there has been no previous learning or entry of probabilities by an expert the network
135. tions An example of one is illustrated in figure 10 1 Below the meter is the node s name title or both depending on what was chosen using the Style Node submenu The two states are printed at the bottom of the meter on the left and right The needle indicates the relative belief in each state For the rightmost state the left end of the scale corresponds to a belief probability of 0 and the right end to 100 The 50 point is when the needle is vertical so the center of the scale is marked with a tick If the belief is certainty due to a finding for this node then the needle will be all the way to one side and the background gray of the meter will be darkened If the current position of the needle is invalid for the findings entered probably because the latest findings haven t been taken into account yet the needle will be drawn as a dotted line 79 If the belief meter style is used for a node with more than two states then all the states except the first will be grouped together and will be called Other The first state will be rightmost on the meter so its belief will be well represented by the needle 0 full left and 100 full right 11 4 Net Styles The Style gt Net submenu allows you to choose the way network links are displayed Style gt Net Hide Links allows you to hide all the links in the network This is especially useful when you are creating something for an end user who will make queries to the network
136. u 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 This section deals with join trees see chapter 8 for information on node absorption 2 5 Example Belief Network Now let s look at an example of using Netica to do probabilistic inference In this example we will read in a simple network from a file compile it into a form suitable for fast inference enter some findings and see how the beliefs of various nodes change with each finding The network we will use is shown below Although reasonable it is a toy medical diagnosis example from LauritzenSpiegelhalter88 that has often been used in the past for demonstration purposes To a certain degree the links of the network 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 symptoms for the disease Tuberculosis Tuberculosis or Cancer You can read it in to Netica by doing a File Open menu command in this document menu selections are indicated in bold with arrows indicating choices or submenus so the previous means choose Open from the File menu When the standard file opening dialog box lt 20 appears use it to open the file called Asia This file is included with the Netica distribution in the Examples folder 2 4 Compiling a Belief Network To c
137. ufmann San Mateo CA Heckerman David Abe Mamdani and Michael P Wellman 1995 Real world applications of Bayesian networks in Communications of the ACM 38 3 24 26 Introduction to this special issue of CACM on belief networks Henrion Max John S Breese and Eric J Horvitz 1991 Decision Analysis and Expert Systems in AI Magazine Winter 1991 12 4 64 91 Lauritzen Steffen L and David J Spiegelhalter 1988 Local computations with probabilities on graphical structures and their application to expert systems in J Royal Statistics Society B 50 2 157 194 Matheson James E 1990 Using Influence diagrams to value information and control in Influence Diagrams Belief Nets and Decision Analysis Robert M Oliver and J Q Smith eds John Wiley amp Sons Chichester Neapolitan Richard E 1990 Probabilistic Reasoning in Expert Systems Theory and Algorithms John Wiley amp Sons New York 83 Pearl Judea 1988 Probabilistic Reasoning in Intelligent Systems Networks of Plausible Inference Morgan Kaufmann San Mateo CA 2nd edition 1991 Qi Runping 1994 Decision graphs Algorithms and applications to influence diagram evaluation and high level path planning under uncertainty PhD Thesis Dept of Computer Science Univ of British Columbia Canada Also Tech Report 94 27 Dept of Computer Science Univ of British Columbia Qi Runping and David Poole 1995 New method for influen
138. ure from the dialog and perhaps remove the check from float over text Sometimes Word does not do a perfect job of converting it but just double clicking on the graphic to bring up the picture editor and then closing it again without making any changes seems to fix any imperfections If you want to paste a network into a bitmap program such as Paint which comes with Windows 95 it is recommended that you use Alt PrintScreen to make a file containing the network graphics i e a screen dump and read that into the bitmap program 11 6 Printing You can print a network on a printer with the File Print menu command First you may want to do File Printer Setup to select printing options such as page size margins magnification reduction and which printer to use If the network diagram is larger than one page then the printer will print parts of it on multiple pages in such a way that the pages can be trimmed and then attached together to produce the overall diagram If you wish to see what part of the diagram will end up on which page you can turn on the page breaks by choosing the menu entry Layout Show Page Breaks if it is not already checked This will draw a light blue line at the page divisions Choosing it again will turn off the page break display When you change the magnification reduction or margins etc using File Printer Setup the page break lines will shift showing how much fits on each page
139. w Netica also has a Network Compile Optimize command which spends a long time working out a very efficient structure for the internal join tree As it is working it displays in the Messages window the memory requirements and projected inference time to do a belief updating with the best structure it has developed so far The memory requirements are exact but the inference time is only approximate it is based on doing the inference using the same computer as the one doing the compiling on having enough memory installed that it doesn t need to use virtual memory and on having a large share of the processor time under multitasking Press the 21 Ctrl key and hold down the left mouse button at the same time when you are satisfied with the structure it has found and you want it to stop trying to find a better one For those interested in a technical explanation the quick compile does a minimum weight search for a good elimination order and the optimized compile searches for the best elimination order using a specialized algorithm which is a combination of minimum weight search and stochastic search with some facets of multi start methods simulated annealing and genetic algorithms If you save a compiled network to file then when you read it back the next time you will have to recompile it However you may still want to save a network after compiling it since some information gets saved with the network to make compiling go faster the ne
140. will get the pop up menu for changing the cell s value You can drag below or above the window to force automatic scrolling Also you can extend or reduce a selection by holding down the shift key when you click in another cell After you have selected some cells you can copy their values to the clipboard by doing an Edit Copy command If you want to place those values in some other cells you select the other cells and then do an Edit Paste command When you paste the number of rows and columns of cells selected must be the number of rows and columns in the clipboard i e the same as the number of rows and columns selected when you originally did the Edit gt Copy command You can copy cell values from a spreadsheet or word processor to the clipboard and then paste them into a Netica array of cells or vice versa When you paste values into Netica cells the number of rows and columns in the clipboard must match the number of selected Netica cells If the data you are pasting consists of probabilities expressed as decimal fractions e g 0 25 rather than percentages e g 25 then you should do a normalize command see the following section after pasting When you copy Netica cells to the clipboard they are entered as text with a tab between each entry on the same line and a carriage return line feed pair between lines and at the end of the last line If you copy from a word processor or text editor to Netica the format should
141. works is published within the artificial intelligence AI community it is really the combined work of the statistics probability decision analysis operations research and AI communities Many of the researchers who developed the theory of belief and decision networks attended the annual Uncertainty in Artificial Intelligence conference from 1985 to present and so advanced material can be found in the conference proceedings published by North Holland and Morgan Kaufmann In 1988 Judea Pearl wrote Probabilistic Reasoning in Intelligent Systems which was the most influential and widely cited book in the development of belief networks It is an excellent foundational book but it doesn t contain the latest developments and has a very mathematical and theoretical orientation Then in 1990 Richard Neapolitan wrote Probabilistic Reasoning in Expert Systems Theory and Algorithms which is a little more modern and easier to read but is limited in scope and is most useful to someone building a probabilistic reasoner from the ground up or better yet teaching a course on how to do that It is suitable if you want to spend some serious time studying to understand many of the algorithms used internally in Netica for a quick study read Spiegelhalter amp DL C93 Russell amp N95 is a rather complete and excellent introductory textbook for artificial intelligence that does a good job of describing Bayes networks decision networks dynamic decisio
142. xt time it is read back If you save a belief network after an optimized compile then the next time you open it the quick compile command will give it the optimized structure quickly as long as you don t change the network nodes or links in between 2 5 Entering and Retracting Findings A compiled belief network is ready to apply to a new case As details of the case arrive you can enter them as findings also known as evidence Of course you would not mix findings from one case with those of another When you know the value for some node you can enter it as a finding by clicking on it with the right mouse button A pop up menu will appear known as the findings pop up menu with each possible state of the node as a menu entry Using it you can enter the finding A faster method which works when the network is compiled and the node is displayed in belief bar or belief meter style is to do a regular click directly on the name of the finding you wish to enter After the finding has been entered the node will be darkened If the node is displayed in belief bar style then a solid outlined bar is drawn for the state matching the finding It does not matter in what order you enter a set of findings If you wish to retract a finding that you have entered for some node choose Unknown from its findings pop up menu or click again directly on the name of the finding of a belief bar node Entering a finding and retracting it is equivalen

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