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

lights no oil no gas starter broken battery age alternator broken fanbelt broken battery dead no charging battery flat gas gauge fuel line blocked

• il light

battery meter car won’t start dipstick

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?

.001

P(B)

.002

P(E)

Alarm Earthquake MaryCalls JohnCalls Burglary

B

T T F F

E

T F T F .95 .29 .001 .94

P(A|B,E) A

T F .90 .05

P(J|A) A

T F .70 .01

P(M|A)

Günay Ch 13–14 Notes

Burglary or Earthquake?

Günay Ch 13–14 Notes