lecture16

# lecture16 - Articial Intelligence Bayes Nets Nilsson...

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Bayes Nets; page 1 of 21 Artiﬁcial Intelligence Bayes Nets Russell and Norvig - Chapter 14 Nilsson - Chapter 19

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Bayes Nets; page 2 of 21 print troubleshooter (part of Windows 95)
Bayes Nets; page 3 of 21 joint probability distributions E1 E2 E3 E4 E5 D1 D2 D3 TTTTTTTT 0.05 TTTTTTTF 0.03 ... ... ... ... ... ... ... ... ... P(D1 | E1, NOT E3) - inefﬁcient for reasoning - hard to acquire the probabilities make use of independence inherent in the domain expert systems: medicine, Microsoft Bayes nets = belief nets

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Bayes Nets; page 4 of 21 Bayes net B T T F F E T F T F P(A) .95 .29 .001 .001 P(B) .002 P(E) Alarm Earthquake MaryCalls JohnCalls Burglary A P(J) T F .90 .05 A P(M) T F .70 .01 .94 = directed acyclic graph with conditional probability tables nodes = random variables, links = direct inﬂuences this really means P(A=T|B=T,E=T)
Bayes Nets; page 5 of 21 conditional probability tables “AND” XY X T T F F Y T F T F P(“AND” | X, Y) 1.0 0.0 0.0 0.0 COIN P(COIN) 0.5

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Bayes Nets; page 6 of 21 from Bayes nets to joint probability distributions B T T F F E T F T F P(A) .95 .29 .001 .001 P(B) .002 P(E) Alarm Earthquake MaryCalls JohnCalls Burglary A P(J) T F .90 .05 A P(M) T F .70 .01 .94 Burglary Earthquake Alarm JohnCalls MaryCalls TT T T T P(B, E, A, J, M) = P(B) P(E) P(A | B,E) P( J | A) P(M | A) 0.000001197
Bayes Nets; page 7 of 21 from joint probability distributions to Bayes nets (1) repeatedly: - pick a variable - condition it on the smallest possible set of variables picked previously A T T T T F F F F B T T F F T T F F C T F T F T F T F 0.054 0.126 0.002 0.018 0.432 0.288 0.032 0.048 P(A, B, C) = P(A) P(B | A) P(C | B,A) A order: A, B, C C B P(A) 0.2 A T F P(B) 0.9 0.9 A T T F F B T F T F P(C) 0.3 0.1 0.6 0.4

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lecture16 - Articial Intelligence Bayes Nets Nilsson...

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