1. CS 221: Artificial Intelligence Lecture 3: Probability and Bayes Nets Sebastian Thrun and Peter Norvig Naranbaatar Bayanbat, Juthika Dabholkar, Carlos Fernandez-Granda, Yan Largman, Cameron Schaeffer, Matthew Seal Slide Credit: Dan Klein (UC Berkeley)

16. Example: Independence? T W P warm sun 0.4 warm rain 0.1 cold sun 0.2 cold rain 0.3 T W P warm sun 0.3 warm rain 0.2 cold sun 0.3 cold rain 0.2 T P warm 0.5 cold 0.5 W P sun 0.6 rain 0.4

18. Bayes Network Representation Cavity Catch Toothache P(cavity) P(catch | cavity) P(toothache | cavity) 1 parameter 2 parameters 2 parameters Versus: 2 3 -1 = 7 parameters

19. A More Realistic Bayes Network

20. Example Bayes Network: Car

27. Example: Coin Flips X 1 X 2 X n Only distributions whose variables are absolutely independent can be represented by a Bayes ’ net with no arcs. h 0.5 t 0.5 h 0.5 t 0.5 h 0.5 t 0.5

28. Example: Traffic R T +r 1/4  r 3/4 +r +t 3/4  t 1/4  r +t 1/2  t 1/2 R T joint +r +t 3/16 +r -t 1/16 -r +t 3/8 -r -t 3/8

29. Example: Alarm Network B urglary E arthqk A larm J ohn calls M ary calls How many parameters? 1 1 4 2 2 10

30. Example: Alarm Network B urglary E arthqk A larm J ohn calls M ary calls B P(B) +b 0.001  b 0.999 E P(E) +e 0.002  e 0.998 B E A P(A|B,E) +b +e +a 0.95 +b +e  a 0.05 +b  e +a 0.94 +b  e  a 0.06  b +e +a 0.29  b +e  a 0.71  b  e +a 0.001  b  e  a 0.999 A J P(J|A) +a +j 0.9 +a  j 0.1  a +j 0.05  a  j 0.95 A M P(M|A) +a +m 0.7 +a  m 0.3  a +m 0.01  a  m 0.99

31. Example: Alarm Network B urglary E arthquake A larm J ohn calls M ary calls

40. Example Yes R T B T ’

41. Example R T B D L T ’ Yes Yes Yes

43. A Common BN T 1 T 2 A T N T 3 … Unobservable cause Tests time Diagnostic Reasoning:

44. A Common BN T 1 T 2 A T N T 3 … Unobservable cause Tests time Diagnostic Reasoning:

45. A Common BN T 1 T 2 A T N T 3 … Unobservable cause Tests time Diagnostic Reasoning:

46. A Common BN T 1 T 2 A T N T 3 … Unobservable cause Tests time Diagnostic Reasoning: