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CS498-EA Reasoning in AI Lecture #2

CS498-EA Reasoning in AI Lecture #2. Professor: Eyal Amir Fall Semester 2009. Today. Applications of reasoning in AI Econometrics Social Networks Verification of Circuits and Programs Natural Language Processing Robotics Vision Computer Security.

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CS498-EA Reasoning in AI Lecture #2

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  1. CS498-EAReasoning in AILecture #2 Professor: Eyal Amir Fall Semester 2009

  2. Today • Applications of reasoning in AI • Econometrics • Social Networks • Verification of Circuits and Programs • Natural Language Processing • Robotics • Vision • Computer Security

  3. 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)

  4. Experiments

  5. Experiments

  6. 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)

  7. 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

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

  9. 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

  10. 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

  11. 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

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

  13. Robotics • Videos

  14. Vision • Videos

  15. Computer Security • Shortest paths

  16. Finding the “best” path between two points • Classic computer science problem: many algorithms, applications • “best” generally means minimizing some sort of cost each edge has some cost associated with it cost of path generally sum etc. of cost of edges along path 10 10 10 source s 10 sink t

  17. Stochastic setting • Edges fail probabilistically • Goal: find most reliable path Directed Acyclic Graph G edge reliability t 0.85 s 0.9 0.95 path reliability = 0.95 x 0.9 x 0.85 = 0.73 assumption: independent!!! not very realistic...

  18. Stochastic setting • Consider a richer structure using a graphical model (discrete) hidden variable X t e3 s e2 e1 the hidden variable allows us to model correlations and dependencies between edge failures binary random variables: 1 if edge survives, 0 if edge fails

  19. Stochastic setting • Specified: • prior probability on X • conditional probabilities for each edge Pr[X=1] = 0.4 Pr[X=2] = 0.1 Pr[X=3] = 0.2 Pr[X=4] = 0.3 Pr[e1 survives | X=1] = 0.9 Pr[e1 fails | X=1] = 0.1 ... etc. X t e3 s e2 e1

  20. Stochastic setting • Graphical model defines joint distribution: Pr[X,e1,e2,e3,...] = Pr[X] Pr[e1|X] Pr[e2|X]... • Reliability of path is marginal Pr[e1,e2,e3] • Can compute by summing... X t e3 s e2 e1

  21. Many applications • Just to name a few: • Network QoS routing[citations] routers fail stochastically links fail stochastically Failures are typically correlated: if two machines run the same version of unpatched Windows, and one gets infected by a virus...

  22. Many applications • Just to name a few: • Network QoS routing [citations] • Parsing w/ weighted FSAs FSA where edges have probabilities assigned to them (from Smith + Eisner ACL’05 best paper)

  23. Many applications • Just to name a few: • Network QoS routing • Parsing w/ weighted FSAs • Robot navigation e.g., DARPA Grand Challenge

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