Plan Recognition with Multi-Entity Bayesian Networks

Kathryn Blackmond Laskey

Department of Systems Engineering and Operations ResearchGeorge Mason University

Dagstuhl Seminar April 2011

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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

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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 worlds is 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

R E I W T B S PrT T T T T T T p1

T T T T T T F p2

T T T T T F T p3

…

Nuclear Weapons (W)

StealMaterials (S)

BuyReactors (B)

RegionalDomination (R)

Exercise (E)

TroopsMoving (T)

Invasion (I)

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)

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First-Order Logic & Probabilty• A first-order probabilistic logic also assigns probabilities to

sets of possible worlds• A first-order possible world (aka structure) 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 logic assigns a probability measure to first-order structures– This is called “measure model”

semantics (Gaifman,1964)Charniak and Goldman (1993)

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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

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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

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Example: Maritime Domain Awareness

Entities, attributes and relations

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MTheory for Maritime Domain Awareness

Built in UnBBayes-MEBN

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MDA SSBN

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

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Protégé Plugin for UnBBayes

(coming soon)

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Drag-and-Drop OWL Properties

drag-and-drop

(coming soon)

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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/