Korb K.B., Nicholson A.E. Bayesian Artificial Intelligence
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5.5.1 NAGarchitecture
5.5.2 Example:Anasteroidstrike
5.5.3 Thepsychologyofinference
5.5.4 Example:Theasteroidstrikecontinues
5.5.5 Thefutureofargumentation
5.6 Summary
5.7 Bibliographicnotes
5.8 Problems
Part II LEARNING CAUSAL MODELS
Chapter 6 Learning Linear Causal Models
6.1 Introduction
6.2 Pathmodels
6.2.1 Wright’s first decomposition rule
6.2.2 Parameterizinglinearmodels
6.2.3 Learninglinearmodelsiscomplex
6.3 Conditionalindependencelearners
6.3.1 Markovequivalence
6.3.2 PCalgorithm
6.3.3 Causaldiscoveryversusregression
6.4 Summary
6.5 Bibliographicnotes
6.6 Technicalnotes
6.7 Problems
Chapter 7 Learning Probabilities
7.1 Introduction
7.2 Parameterizingdiscretemodels
7.2.1 Parameterizingabinomialmodel
7.2.2 Parameterizingamultinomialmodel
7.3 Incompletedata
7.3.1 TheBayesiansolution
7.3.2 Approximatesolutions
7.3.3 Incompletedata:summary
7.4 Learninglocalstructure
7.4.1 Causalinteraction
7.4.2 Noisy-orconnections
7.4.3 Classificationtreesandgraphs
7.4.4 Logitmodels
7.4.5 Dualmodeldiscovery
7.5 Summary
7.6 Bibliographicnotes
7.7 Technicalnotes
7.8 Problems
© 2004 by Chapman & Hall/CRC Press LLC
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Chapter 8 Learning Discrete Causal Structure
8.1 Introduction
8.2 Cooper & Herskovits’ K2
8.2.1 Learningvariableorder
8.3 MDLcausaldiscovery
8.3.1 Lam and Bacchus’s MDL code for causal models
8.3.2 Suzuki’sMDLcodeforcausaldiscovery
8.4 Metricpatterndiscovery
8.5 CaMML:CausaldiscoveryviaMML
8.5.1 AnMMLcodeforcausalstructures
8.5.2 AnMMLmetricforlinearmodels
8.6 CaMMLstochasticsearch
8.6.1 Geneticalgorithm(GA)search
8.6.2 Metropolissearch
8.6.3 Priorconstraints
8.6.4 MMLmodels
8.6.5 AnMMLmetricfordiscretemodels
8.7 Experimentalevaluation
8.7.1 Qualitative evaluation
8.7.2 Quantitative evaluation
8.8 Summary
8.9 Bibliographicnotes
8.10 Technicalnotes
8.11 Problems
Part III KNOWLEDGE ENGINEERING
Chapter 9 Knowledge Engineering with Bayesian Networks
9.1 Introduction
9.1.1 Bayesiannetworkmodelingtasks
9.2 TheKEBNprocess
9.2.1 KEBNlifecyclemodel
9.2.2 PrototypingandspiralKEBN
9.2.3 AreBNssuitableforthedomainproblem?
9.2.4 Processmanagement
9.3 Modelingandelicitation
9.3.1 Variablesandvalues
9.3.2 Graphicalstructure
9.3.3 Probabilities
9.3.4 Localstructure
9.3.5 VariantsofBayesiannetworks
9.3.6 Modelingexample:missingcar
9.3.7 Decisionnetworks
9.4 Adaptation
9.4.1 Adaptingparameters
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9.4.2 Structuraladaptation
9.5 Summary
9.6 Bibliographicnotes
9.7 Problems
Chapter 10 Evaluation
10.1 Introduction
10.2 Elicitationreview
10.3 Sensitivityanalysis
10.3.1 Sensitivitytoevidence
10.3.2 Sensitivitytochangesinparameters
10.4 Case-basedevaluation
10.4.1 Explanation methods
10.5 Validation methods
10.5.1 Predictive accuracy
10.5.2 Expectedvalue
10.5.3 Kullback-Leiblerdivergence
10.5.4 Informationreward
10.5.5 Bayesianinformationreward
10.6 Summary
10.7 Bibliographicnotes
10.8 Technicalnotes
10.9 Problems
Chapter 11 KEBN Case Studies
11.1 Introduction
11.2 Bayesianpokerrevisited
11.2.1 The initial prototype
11.2.2 Subsequentdevelopments
11.2.3 Ongoing Bayesian poker
11.2.4 KEBNaspects
11.3 An intelligent tutoring system for decimal understanding
11.3.1 TheITSdomain
11.3.2 ITSsystemarchitecture
11.3.3 Expertelicitation
11.3.4 Automated methods
11.3.5 Fieldtrialevaluation
11.3.6 KEBNaspects
11.4 Seabreeze prediction
11.4.1 The seabreeze prediction problem
11.4.2 Thedata
11.4.3 Bayesiannetworkmodeling
11.4.4 Experimentalevaluation
11.4.5 KEBNaspects
11.5 Summary
© 2004 by Chapman & Hall/CRC Press LLC
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Appendix A Notation
Appendix B Software Packages
B.1 Introduction
B.2 History
B.3 Murphy’s Software Package Survey
B.4 BNsoftware
B.4.1 Analytica
B.4.2 BayesiaLab
B.4.3 BayesNetToolbox(BNT)
B.4.4 GeNIe
B.4.5 Hugin
B.4.6 JavaBayes
B.4.7 MSBNx
B.4.8 Netica
B.5 Bayesianstatisticalmodeling
B.5.1 BUGS
B.5.2 FirstBayes
B.6 Causaldiscoveryprograms
B.6.1 BayeswareDiscoverer
B.6.2 CaMML
B.6.3 TETRAD
B.6.4 WinMine
References
© 2004 by Chapman & Hall/CRC Press LLC
List of Figures
1.1 (a) The event space U; (b) ;(c)
1.2 Conditional probability:
1.3 Reverend Thomas Bayes (1702–1761)
2.1 ABNforthelungcancerproblem
2.2 Typesofreasoning
2.3 Alternative structures from different node orderings
2.4 (a) Causal chain; (b) common cause; (c) common effect.
2.5 Threetypesofblockingsituations.
2.6 Pearl’s Earthquake BN.
2.7 MetastaticcancerBN
2.8 AlternativeBNsforthe“Asia”example.
2.9 AquickguidetousingNetica.
3.1 A generic polytree with message passing parameters and messages.
3.2 Extended earthquake BN
3.3 Message passing algorithm: initialization,
and messages.
3.4 Messagepassingalgorithm:propagationstages
3.5 Virtual node for uncertain evidence.
3.6 Using a virtual node in the earthquake BN
3.7 A multiply-connected BN: metastatic cancer.
3.8 AdhocclusteringofmetastaticcancerBN
3.9 Different clusterings of a multiply-connected BN.
3.10 Junction tree algorithm (a) the moral graph (b) the junction tree.
3.11 Structures created by junction tree algorithm application.
3.12 Comparison of LS, LW approximate inference algorithms.
3.13 Modelingcausalinterventions.
3.14 AquickguidetousingHugin.
3.15 AddingvirtualevidenceinNeticaandHugin.
4.1 The utility of money.
4.2 Decision network node types.
4.3 Adecisionnetworkforthefootballteamexample.
4.4 Footballdecisionnetworkwithinformationlink.
4.5 Adecisionnetworkforthefeverexample.
4.6 Decision networks: (a) non-intervening (b) intervening actions.
© 2004 by Chapman & Hall/CRC Press LLC
4.7 Decision network for a test-action sequence of decisions.
4.8 Decision network for the real estate investment example.
4.9 Decision tree evaluation for real estate investment example.
4.10 GeneralstructureofaDBN.
4.11 DBNforthefeverexample.
4.12 DBN maintained as a sliding “window” of two time-slices.
4.13 Arcreversal.
4.14 A generic DDN.
4.15 DDNstructureforthefeverexample.
4.16 A DDN for the mobile robot example.
5.1 Generic BN structures for medical diagnosis
5.2 TheALARMBNforICUmonitoring.
5.3 TheHailfinderBN.
5.4 TheBATmobileBN.
5.5 Adecisionnetworkforpoker.
5.6 Betting curve for folding.
5.7 DBNforambulationmonitoringandfalldetection.
5.8 Extending DBN with sensor status node.
5.9 NAGarchitecture
5.10 AsteroidBayesiannetwork.
5.11 Asteroidargumentgraph.
5.12 NAGcombinessemanticandBayesiannetworks.
6.1 (a) Causal chain; (b) common cause; (c) common effect.
6.2 Alinearmodel.
6.3 OECDpubliceducationspendingmodel.
6.4 Non-standardized OECD public education spending model.
6.5 Causalmodelforcollegeplans.
6.6 Causal model for college plans learned after CI Principle I.
6.7 Alternativecausalmodelforcollegeplans.
6.8 Allpatternsinthreevariables.
7.1 Updatingabinomialestimate
7.2 Twobetadistributions:B(2,2)andB(2,8).
7.3 Twobetadistributions:B(10,10)andB(10,16).
7.4 Anoisy-ormodel.
7.5 Aclassificationtreeforacidandalkali.
7.6 Aclassificationgraphforacidandalkali.
8.1 Shannon’s information measure.
8.2 AMarkovequivalent:(a)chain;(b)commoncause
9.1 AKEBNlifecyclemodel.
9.2 AspiralmodelforKEBN.
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9.3 Matilda’s visualization and explanation of d-separation.
9.4 ABNsolutionforthefirealarmexample.
9.5 Matilda’s Type 1 visualization.
9.6 Matilda’s Type 2 visualization.
9.7 Matilda’s Type 3 visualization.
9.8 Overconfidencecurve.
9.9 VE elicitation and verbal map editing windows.
9.10 Visual aids for probability elicitation.
9.11 Different qualitative causal relationships.
9.12 LocalstructureforCPTs
9.13 Divorcingexample.
9.14 Divorcinginsearchandrescueproblem
9.15 Missingcarproblem:preliminaryanalysis.
9.16 AlternativeBNsforthemissingcarproblem.
9.17 Adecisionnetworkforthemissingcarproblem.
10.1 Adecisionnetworkforthecancerexample.
10.2 Adecisionnetworkfordiseasetreatment.
10.3 Evaluationoftest-treatmentnetwork.
10.4 Sensitivityanalysisforadecision.
10.5 KLdivergence.
10.6 Good’s information reward.
11.1 TheevolutionofBPPnetworks.
11.2 Intelligent tutoring system architecture.
11.3 AscreenfromtheITS“FlyingPhotographer”game.
11.4 DecimalITSelicitedBN.
11.5 Seabreeze development cycle.
11.6 Existingrule-basedsystempseudocode.
11.7 Seabreeze prediction BNs - elicited and learnt.
11.8 Comparison of RB predictive accuracy.
11.9 Wind direction predictive accuracy.
11.10 Incrementalpararmeterlearningresults.
B.1 Features used in Murphy’s software comparison.
© 2004 by Chapman & Hall/CRC Press LLC
List of Tables
2.1 Nodesandvaluesforthelungcancerexample
2.2 Updatedbeliefsgivennewinformation
4.1 Decisions for football team given Forecast
4.2 Decisionscalculatedforthefeverproblem
4.3 Decisionforrealestateinvestmentproblem
5.1 Poker hand types: weakest to strongest
5.2 Poker action/outcome utilities
5.3 AmbulationmonitoringDBNCPTs
5.4 ChangingbeliefsfortheambulationmonitoringDBN
5.5 New CPTs with sensor status node added
7.1 Exampleofincompletedata
7.2 CPT for Severe Cough generated from noisy-or parameters
7.3 CPTforthefirst-orderlogitmodel
9.1 Alternative discretizations of an Age node
9.2 Discretization based on child node distributions
9.3 Incoherent qualitative assessments for the X-ray CPT
9.4 Utility table for the missing car problem
9.5 Expected utilities for the missing car problem
10.1Entropyandvariancemeasuresforthreedistributions
10.2OutputfromNetica’ssensitivitytofindingsfunction
10.3 Expected utilities for
inlungcancerproblem
10.4 Expected utilities given different test findings
10.5 Utilities for binary classification and misclassification
11.1 Misconceptions about decimals
11.2ComparisongridforITSevaluation
11.3Fineclassificationsummarymodelcomparison.
B.1 Software packages: name, Web location and developers (part I)
B.2 Software packages: name, Web location and developers (part II)
B.3 Murphy’s feature comparison of software packages
© 2004 by Chapman & Hall/CRC Press LLC
Notation
A few remarks about notation before we begin. The notation special to Bayesian
networks (or to our treatment of them) will be introduced as we proceed; first in-
troductions of notation (and acronyms) will be recorded, with page numbers, in Ap-
pendix A. General mathematical notation is listed on the next page.
Here we describe the simplest aspects of the notation we adopt. First, variables
(nodes in the network) will be named, with the names being capitalized and usually
italicized (e.g., Y, Alarm, Cancer). Sets of variables will be set in boldface (e.g.,
). The values that variables take will not be capitalized, but will be italicized;
thus, to assert that the alarm is on, we might write Alarm = on. Values abbreviated
to single letters, such as True (T) and False (F), however, will be capitalized. Where
no confusion is likely to arise, variables and values may be abbreviated.
When first introducing new terminology we shall employ boldface to point it out;
thus, for example, the first appearance (after this) of “Bayesianism” will be in bold-
face.
When the identity of the evidence or observation nodes is of interest in an example
figure, they will be shown shaded in the network.
© 2004 by Chapman & Hall/CRC Press LLC
Basic Notation
is a proper subset of
is a proper subset of or equal to
set with all elements of removed
the empty set
the union of and
the intersection of and
is a member of set
the number of objects in set
a set of sets indexed by
the union of all
or
and
is equivalent to
not
for all
factorial
Avariable
The variable takes value
(prior, marginal) probability of
probability that takes value
probability of given evidence
posterior distribution over
set of parent nodes of
an undirected link
a directed link
assignment
the expected value of
the expected value of
the expected utility of action , given evidence
the utility of outcome , given action
the integral of from to
the sum of indexed by
the product of indexed by
The number of ways of taking a subset of j objects from a set of size n
© 2004 by Chapman & Hall/CRC Press LLC