MIT 16 412J - Intro to Probabilistic Relational Models (35 pages)

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Intro to Probabilistic Relational Models



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Intro to Probabilistic Relational Models

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Pages:
35
School:
Massachusetts Institute of Technology
Course:
16 412j - Cognitive Robotics
Cognitive Robotics Documents

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Intro to Probabilistic Relational Models James Lenfestey with Tom Temple and Ethan Howe Intro to Probabilistic Relational Models p 1 24 Outline Motivate problem Define PRMs Extensions and future work Intro to Probabilistic Relational Models p 2 24 Our Goal Observation the world consists of many distinct entities with similar behaviors Exploit this redundancy to make our models simpler This was the idea of FOL use quantification to eliminate redundant sentences over ground literals Intro to Probabilistic Relational Models p 3 24 Example A simple domain a set of students S s1 s2 s3 a set of professors P p1 p2 p3 Well Funded Famous P true f alse Student Of S P true f alse Successful S true f alse Intro to Probabilistic Relational Models p 4 24 Example A simple domain We can express a certain self evident fact in one sentence of FOL s S p P Famous p and Student Of s p Successful s Intro to Probabilistic Relational Models p 5 24 Example A simple domain The same sentence converted to propositional logic p1 f amous and student o f s1 p1 or s1 success f ul and p1 f amous and student o f s2 p1 or s2 success f ul and p1 f amous and student o f s3 p1 or s3 success f ul and p2 f amous and student o f s1 p1 or s1 success f ul and p2 f amous and student o f s2 p1 or s2 success f ul and p2 f amous and student o f s3 p1 or s3 success f ul and p3 f amous and student o f s1 p1 or s1 success f ul and p3 f amous and student o f s2 p1 or s2 success f ul and p3 f amous and student o f s3 p1 or s3 success f ul Intro to Probabilistic Relational Models p 6 24 Our Goal Unfortunately the real world is not so clear cut Need a probabilistic version of FOL Proposal PRMs Propositional Logic Bayes Nets First order Logic PRMs Intro to Probabilistic Relational Models p 7 24 Defining the Schema The world consists of base entities partitioned into classes X1 X2 Xn Elements of these classes share connections via a collection of relations R1 R2 Rm Each entity type is characterized by a set of attributes



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