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CS498-EA Reasoning in AI Lecture #14

CS498-EA Reasoning in AI Lecture #14. Professor: Eyal Amir Fall Semester 2009. * Some slides due to Fei-Fei Li (Stanford U). Summary So Far in Our Class. We saw motivating applications We discussed two methods for propositional-logical reasoning

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CS498-EA Reasoning in AI Lecture #14

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  1. CS498-EAReasoning in AILecture #14 Professor: Eyal Amir Fall Semester 2009 * Some slides due to Fei-Fei Li (Stanford U)

  2. Summary So Far in Our Class • We saw motivating applications • We discussed two methods for propositional-logical reasoning • We studied properties of graphical models of probability distributions • We learned 2 kinds of probabilistic inference methods in graphical models • We examined 2 methods for learning parameters of graphical models

  3. The Road Ahead in Our Class • Variational Approximations • Models and inference with dynamic (temporal) systems: logical, probabilistic • More expressive representations and inference: • First-Order Logic (FOL) • Relational/First-Order Probabilistic Models • Semantic Web and Description Logics • Cross-cutting issues

  4. Before we Continue… • Applications of methods we’ve learned • Review ideas and techniques • Reinvigorate our search for more methods…

  5. Memories from Lecture 2… • Applications of reasoning in AI • Econometrics • Social Networks • Verification of Circuits and Programs • Natural Language Processing • Robotics • Vision • Computer Security

  6. Econometrics Example: A Recession Model of a country • What is probability of recession, when a bank(bm) goes into bankruptcy? • Recession: Recession of a country in [0,1] • Market[X]: Quarterly market (X) index • Loss[X,Y]: Loss of a bank (Y) in a market (X) • Revenue[Y]: Revenue of a bank (Y)

  7. Experiments

  8. Experiments

  9. Social Networks Example: school friendships and their effects Friend(A,B) Attr(A) Measuremt(A) shorthand for Friend(., .), Atrr(.), and Measuremt(.) potential func­tions Friend(A,C) Attr(B) Measuremt(B) Friend(B,C) Attr(C) Measuremt(C)

  10. hlia blia hjoe htom hbob btom hann bjoe bann bbob hval bval f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f tom; val bob; lia lia; tom ann; lia ann; tom lia; ann val; bob tom; ann joe; val ann; joe val; joe tom; lia bob; val lia; joe bob; tom val; tom joe; ann ann; bob val; lia joe; bob tom; bob joe; tom tom; joe joe; lia bob; ann lia; val val; ann ann; val lia; bob bob; joe

  11. Scaling-Up: Computing Pr(f(x,y)) Figure 5: Computation time for

  12. Application: Hardware Verification f3 x1 f1 not AND x2 f5 AND not f2 OR x3 f4 Question: Can we set this boolean cirtuit to TRUE? f5(x1,x2,x3) = a function of the input signal

  13. Application: Hardware Verification f3 x1 f1 not AND x2 f5 AND not f2 OR SAT(f5) ? x3 f4 Question: Can we set this boolean cirtuit to TRUE? f5(x1,x2,x3) = f3 f4 = f1  (f2  x3) = (x1  x2)  (x2  x3) M[x1]=FALSE M[x2]=FALSE M[x3]=FALSE

  14. Hardware Verification • Questions in logical circuit verification • Equivalence of circuits • Arrival of the circuit to a state (required a temporal model, which gets propositionalized) • Achieving an output from the circuit

  15. Natural-Language Processing • Logical semantics • Probabilistic choice between meanings • Inference over time

  16. Vision: Variability within a category Intrinsic Deformation

  17. Constellation model of object categories Burl, Leung, Weber, Welling, Fergus, Fei-Fei, Perona, et al.

  18. Goal

  19. Goal Burl, Leung, et al. ’96 ’98 Weber, Welling, et al. ’98 ’00, Fergus, et al. ‘03

  20. Use prior knowledge of other objects Goal • Estimate uncertainties in models • Do full Bayesian learning • Reduce the number of training examples

  21. Variational Approximation Outline • Motivation • Outline of the Variational Approximation approach • Loopy Belief Propagation • Variational methodology • Sequential approach • Block approach

  22. Variational Inference (in three easy steps…) • Choose a family of variational distributions Q(H). • Use Kullback-Leibler divergence KL(Q||P) as a measure of ‘distance’ between P(H|V) and Q(H). • Find Q which minimises divergence.

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