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Plan Recognition with Multi-Entity Bayesian Networks

Plan Recognition with Multi-Entity Bayesian Networks. Kathryn Blackmond Laskey Department of Systems Engineering and Operations Research George Mason University Dagstuhl Seminar April 2011. Probability and Plan Recognition.

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Plan Recognition with Multi-Entity Bayesian Networks

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  1. Plan Recognition with Multi-Entity Bayesian Networks Kathryn Blackmond Laskey Department of Systems Engineering and Operations Research George Mason University Dagstuhl Seminar April 2011

  2. Probability and Plan Recognition • Probability is a de facto standard for representing and reasoning under uncertainty • Strong theoretical foundation • Unified approach to inference and learning • Combine engineered and learned knowledge • Many general-purpose exact and approximate algorithms • Practical success • Representations and algorithms exploit factored distributions and repeated structure • General case is intractable • Many special case success stories • Finding the right balance between tractability and expressiveness is amajor research challenge

  3. Possible and Probable Worlds • “Traditional or deductive logic admits only three attitudes to any proposition: definite proof, disproof, or blank ignorance.” (Jeffreys) • Semantics of classical logic is based on possible worlds • Set of possible worldsis defined by language, domain, and axioms • In propositional logic, possible worlds assign truth values to atoms (e.g., R  T; W  T; E  F) • Graphical probability model combines propositional logic with probability • Compact representation for implicitly specifying probabilities of sets of possible worlds • Propositional logic + probability is insufficiently expressive for plan recognition Pr(R,E,I,W,T,B,S) = Pr(R)Pr(E)Pr(I|R)Pr(W|R)Pr(T|E,I)Pr(B|W)Pr(S|W)

  4. First-Order Logic & Probabilty • A first-order probabilistic logic also assigns probabilities to sets of possible worlds • A first-order possible world (akastructure)assigns: • each constant symbol to a domain element (e.g., go3  obj23) • each n-ary function symbol to a function on n-tuples of domain elements (e.g., (go-stp pln1)  obj23 • each n-ary relation symbol to a set of n-tuples of domain elements (e.g., inst  {(obj23, go-), (obj78, liquor-store), (obj78, store) … } • A first-order probabilistic logicassigns a probability measure tofirst-order structures • This is called “measure model”semantics (Gaifman,1964) Charniak and Goldman (1993)

  5. Distributions on First-Order Structures • A common approach: • Use parameterized graphical model fragments to define templates for repeated structure • Substitute ground terms for variables and assemble into propositionalized graphical model • Assembly is typically by heuristic procedure • Some computation can be lifted to first-order level • Domain is often assumed finite • This amounts to propositional logic with first-order syntax • Full probabilistic FOL is not even semi-decidable • Research is needed on classes of problems that can be solved

  6. Multi-Entity Bayesian Networks • First-order probabilistic language based on directed graphical models • Similar to plates, PRMs, PBNs • Random variable terms can express any first-order formula • MEBN fragments (MFrags) encode universally quantified directed graphical model fragments • MEBN theory (MTheory) implicitly specifies a joint distribution over first-order structures • Situation-specific Bayesian network (SSBN) construction propositionalizes for inference

  7. Example: Maritime Domain Awareness Entities, attributes and relations

  8. MTheory for Maritime Domain Awareness Built in UnBBayes-MEBN

  9. MDA SSBN Screenshot of situation-specific BN in UnBBayes-MEBN (open-source tool for building & reasoning with PR-OWL ontologies)

  10. Protégé Plugin for UnBBayes (coming soon)

  11. drag-and-drop Drag-and-Drop OWL Properties (coming soon)

  12. UnBBayes-MEBN • Implementation of MEBN (partial) • Stores MFrags as PR-OWL ontology • OWL upper ontology for MEBN theories • PR-OWL 2.0 (to be released soon) has tighter integration between OWL and MEBN • http://pr-owl.org • GUI for defining instances, setting evidence, posing queries (limited to single random variable) • Constructs SSBN • Available on SourceForge • http://sourceforge.net/projects/unbbayes/

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