Bayesian Logic ProgramsContextOutlineSlide 4Bayesian NetworksStud farm (Jensen ´96)Bayesian networks [Pearl ´88]Slide 8Bayesian networks (contd.)From Bayesian Networks to Bayesian Logic ProgramsSlide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Dependency graph = Bayesian networkSlide 19Bayesian Logic Programs - a first definitionBayesian Logic Programs - ExamplesAssociated CPDsCombining RulesCombining Rules (contd.)Bayesian Logic Programs - a definitionSlide 26Discrete-Time Stochastic ProcessTheorem of KolmogorovConsistency ConditionsSupport networkSlide 31Slide 32Slide 33Queries using And/Or treesConsistency Condition (contd.)Relational CharacterBayesian Logic Programs - SummaryApplicationsOther frameworksSlide 40Learning Bayesian Logic ProgramsWhy Learning Bayesian Logic Programs ?What is the data about ?Learning TaskParameter Estimation (contd.)Slide 46Slide 47Slide 48Decomposable CRsSlide 51Slide 52AlgorithmExpectation-MaximizationExperimental EvidenceSlide 56Structural LearningIdea - CLAUDIENSlide 59Claudien - Learning From InterpretationsLearning TaskSlide 62ExampleSlide 64Slide 65Slide 66Slide 67Slide 68Slide 69PropertiesExample ExperimentsConclusionSlide 73Summer School on Relational Data Mining, 17 and 18 August, Helsinki, FinlandK. Kersting, Luc De Raedt, Machine Learning Lab, Albert-Ludwigs-University, Freiburg, GermanyBayesian Logic ProgramsKristian Kersting, Luc De RaedtAlbert-Ludwigs UniversityFreiburg, GermanySummer School on Relational Data Mining 17 and 18 August 2002, Helsinki, FinlandSummer School on Relational Data Mining, 17 and 18 August, Helsinki, FinlandK. Kersting, Luc De Raedt, Machine Learning Lab, Albert-Ludwigs-University, Freiburg, GermanyBayesian Logic Programs Examples and Language Semantics and Support NetworksLearning Data Cases Parameter Estimation Structural Learning ContextReal-world applicationsuncertainty complex, structureddomainslogicobjects, relations,functorsprobability theorydiscrete, continuousBayesian networks Logic Programming (Prolog)+Bayesian logic programsSummer School on Relational Data Mining, 17 and 18 August, Helsinki, FinlandK. Kersting, Luc De Raedt, Machine Learning Lab, Albert-Ludwigs-University, Freiburg, GermanyBayesian Logic Programs Examples and Language Semantics and Support NetworksLearning Data Cases Parameter Estimation Structural Learning Outline•Bayesian Logic Programs•Examples and Language•Semantics and Support Networks•Learning Bayesian Logic Programs•Data Cases•Parameter Estimation•Structural LearningSummer School on Relational Data Mining, 17 and 18 August, Helsinki, FinlandK. Kersting, Luc De Raedt, Machine Learning Lab, Albert-Ludwigs-University, Freiburg, GermanyBayesian Logic Programs Examples and Language Semantics and Support NetworksLearning Data Cases Parameter Estimation Structural Learning Bayesian Logic Programs•Probabilistic models structured using logic •Extend Bayesian networks with notions of objects and relations•Probability density over (countably) infinitely many random variables •Flexible discrete-time stochastic processes•Generalize pure Prolog, Bayesian networks, dynamic Bayesian networks, dynamic Bayesian multinets, hidden Markov models,...Summer School on Relational Data Mining, 17 and 18 August, Helsinki, FinlandK. Kersting, Luc De Raedt, Machine Learning Lab, Albert-Ludwigs-University, Freiburg, GermanyBayesian Logic Programs Examples and Language Semantics and Support NetworksLearning Data Cases Parameter Estimation Structural Learning Bayesian Networks•One of the successes of AI•State-of-the-art to model uncertainty, in particular the degree of belief•Advantage [Russell, Norvig 96]:„strict separation of qualitative and quantitative aspects of the world“•Disadvantge [Breese, Ngo, Haddawy, Koller, ...]:Propositional character, no notion of objects and relations among them Summer School on Relational Data Mining, 17 and 18 August, Helsinki, FinlandK. Kersting, Luc De Raedt, Machine Learning Lab, Albert-Ludwigs-University, Freiburg, GermanyBayesian Logic Programs Examples and Language Semantics and Support NetworksLearning Data Cases Parameter Estimation Structural Learning Stud farm (Jensen ´96)•The colt John has been born recently on a stud farm.•John suffers from a life threatening hereditary carried by a recessive gene. The disease is so serious that John is displaced instantly, and the stud farm wants the gene out of production, his parents are taken out of breeding. •What are the probabilities for the remaining horses to be carriers of the unwanted gene?Summer School on Relational Data Mining, 17 and 18 August, Helsinki, FinlandK. Kersting, Luc De Raedt, Machine Learning Lab, Albert-Ludwigs-University, Freiburg, GermanyBayesian Logic Programs Examples and Language Semantics and Support NetworksLearning Data Cases Parameter Estimation Structural Learning bt_ann bt_brianbt_cecilybt_dorothybt_ericbt_gwennbt_unknown2bt_unknown1bt_fredbt_henry bt_irenebt_johnBayesian networks [Pearl ´88]Based on the stud farm example [Jensen ´96] _bt johnPaSummer School on Relational Data Mining, 17 and 18 August, Helsinki, FinlandK. Kersting, Luc De Raedt, Machine Learning Lab, Albert-Ludwigs-University, Freiburg, GermanyBayesian Logic Programs Examples and Language Semantics and Support NetworksLearning Data Cases Parameter Estimation Structural Learning bt_ann bt_brianbt_cecilybt_dorothybt_ericbt_gwennbt_unknown2bt_unknown1bt_fredbt_henry bt_irenebt_johnBayesian networks [Pearl ´88]Based on the stud farm example [Jensen ´96](Conditional) Probability distribution _bt johnPaP(bt_john) bt_henry bt_irene(1.0,0.0,0.0) aa aa(0.5,0.5,0.0) aa aA(0.0,1.0,0.0) aa AA...(0.33,0.33,0.33) AA AAP(bt_cecily=aA|bt_john=aA)=0.1499 P(bt_john=AA|bt_ann=aA)=0.6906P(bt_john=AA)=0.9909Summer School on Relational Data Mining, 17 and 18 August, Helsinki, FinlandK. Kersting, Luc De Raedt, Machine Learning Lab, Albert-Ludwigs-University, Freiburg, GermanyBayesian Logic Programs Examples and Language Semantics and Support NetworksLearning Data Cases Parameter Estimation Structural Learning Bayesian networks (contd.)•acyclic graphs•probability distribution over a finite set of random variables:1, ,nX XK
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