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Challenge Paper: Marginal Probabilities for Instances and Classes

Challenge Paper: Marginal Probabilities for Instances and Classes. Oliver Schulte School of Computing Science Simon Fraser University Vancouver, Canada. Class-Level and Instance-Level Queries.

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Challenge Paper: Marginal Probabilities for Instances and Classes

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  1. Challenge Paper: Marginal Probabilities for Instances and Classes • Oliver Schulte • School of Computing Science • Simon Fraser University • Vancouver, Canada

  2. Class-Level and Instance-Level Queries • Classic AI research distinguished two types of probabilistic relational queries. (Halpern 1990, Bacchus 1990). Class-level queries Relational Statistics Type 1 probabilities Instance-level queries Ground facts Type 2 probabilities Relational Query Halpern, “An analysis of first-order logics of probability”, AI Journal 1990.Bacchus, “Representing and reasoning with probabilistic knowledge”, MIT Press 1990.

  3. A connection between class-level and instance-level probabilities • Percentage of Flying Birds = 90%. • Halpern: Probability that a typical or random bird flies is 90%. What is the answer to P(Flies(Tweety))? It should be 90%! Marginal Probabilities for Instances and Classes

  4. Halpern’s Instantiation Version • Given that Tweety is a bird (and nothing else), the probability that Tweety flies =the probability that a randomly chosen bird flies.P(Flies(Tweety)|Bird(Tweety)) =P(Flies(B)|Bird(B)). • Assuming that 1st-order variables and constants are typed:P(Flies(Tweety)) =P(Flies(B)). • The Marginal Equivalence Principle.

  5. Marginal Probabilities for Instances and Classesa Four Arguments for Marginal Equivalence

  6. I: Intuitive Plausibility • Used in cold-start problems. • Equivalent to Miller’s principle. Marginal Probabilities for Instances and Classesa

  7. II: Score Maximization Marginal Probabilities for Instances and Classesa

  8. III: Latent Variable Models Satisfy Marginal Equivalence Marginal Probabilities for Instances and Classesa U(S) U(C) intelligence(S) Registered(S,C) diff(C)

  9. IV: Something Else Marginal Probabilities for Instances and Classesa

  10. The Challenge If we accept that an SRL system should satisfy class-instance marginal equivalence, how do we design a system to achieve that? Marginal Probabilities for Instances and Classesa

  11. ParametrizedBayes Net Examples • Proposition If each node in the ground network has a unique set of parents, then class-level marginals = instance-level marginal. • For other structures, it depends on the combining rule/parameters used. diff(C) intelligence(S) Registered(S,C) Marginal Probabilities for Instances and Classesa

  12. Constraints are Good • Pedro Domingos: “The search space for SRL algorithms is very large even by AI standards.” • Class-instance marginal equivalence reduces the search space. • Strong theoretical foundation. • The challenge is to implement the constraint. ParametrizedBayes Nets PBN + Marginal Equivalence Marginal Probabilities for Instances and Classesa

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