CS325 Artificial Intelligence Chs 1314 Notes Cengiz Gnay Spring - PowerPoint PPT Presentation

CS325 Artificial Intelligence Chs 13–14 Notes Cengiz Günay Spring 2013 Günay Ch 13–14 Notes

Probability Cheat Sheet Summation rule: P ( A ) + P ( ¬ A ) = 1 Non-binary: � x P ( A = x ) = 1 Union: P ( A ∨ B ) = P ( A ) + P ( B ) − P ( A ∧ B ) Conditional and joint prob: P ( A | B ) P ( B ) = P ( A , B ) P ( B | A ) P ( A ) = P ( A , B ) Bayes rule: P ( B | A ) = P ( A | B ) P ( B ) P ( A ) Normalize instead of P ( A ) : P ( A ) = P ( A | B ) P ( B ) + P ( A |¬ B ) P ( ¬ B ) because P ( B | A ) + P ( ¬ B | A ) = 1. In general: P ( A | X ) = α � y P ( A , X , y ) Günay Ch 13–14 Notes

Cancer Example with 2 Tests Günay Ch 13–14 Notes

Dependence Independence: X ⊥ Y ⇒ P ( X | Y ) = P ( X ) ⇒ P ( X , Y ) = P ( X ) P ( Y ) Conditional ind: X ⊥ Y | Z ⇒ P ( X | Z , Y ) = P ( X | Z ) Exercises X ⊥ Y | Z ⇔ P ( X ⊥ Y )? Günay Ch 13–14 Notes

Dependence (cont.) Explaining away? Dependence based on outcome: P ( C | A , B ) ⇒ A ⊥ B but not A ⊥ B | C More complex Bayes nets D-separation (reachability); summary of rules joint probability, number of parameters? compactness based on construction Günay Ch 13–14 Notes

Car diagnosis fanbelt alternator battery age broken broken battery no charging dead battery fuel line battery starter no oil no gas flat blocked broken meter car won’t gas gauge lights oil light dipstick start Number of params? Günay Ch 13–14 Notes

Continuous random variables? Natural values Discretization Hybrid Bayes nets Sigmoid and Gaussian Fuzzy logic Günay Ch 13–14 Notes

Burglary or Earthquake? P(E) P(B) Burglary Earthquake .001 .002 B E P(A|B,E) T T .95 Alarm T F .94 F T .29 F F .001 A P(J|A) A P(M|A) T JohnCalls .90 .70 MaryCalls T F .05 F .01 Günay Ch 13–14 Notes

Burglary or Earthquake? Günay Ch 13–14 Notes