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Rushdi Shams, Dept of CSE, KUET, Bangladesh 1
Knowledge RepresentationProbabilistic Logic
Artificial IntelligenceVersion 2.0
Rushdi Shams, Dept of CSE, KUET, Bangladesh 2
Conditional ProbabilityDefinition of conditional probability:
P(a | b) = P(a b) / P(b) if P(b) > 0
Product rule gives an alternative formulation:
P(a b) = P(a | b) P(b) = P(b | a) P(a)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 3
Inference with Probability
Rushdi Shams, Dept of CSE, KUET, Bangladesh 4
Inference in ProbabilityP(toothache) =
0.108 + 0.012 + 0.016 + 0.064 = 0.2
Rushdi Shams, Dept of CSE, KUET, Bangladesh 5
Inference in ProbabilityP(cavity V toothache) =
0.108 + 0.012 + 0.072 + .008 + 0.016 + 0.064 = 0.28
Rushdi Shams, Dept of CSE, KUET, Bangladesh 6
Inference in ProbabilityCan also compute conditional probabilities:
Rushdi Shams, Dept of CSE, KUET, Bangladesh 7
Inference in ProbabilityCan also compute conditional probabilities:
Rushdi Shams, Dept of CSE, KUET, Bangladesh 8
Baye’s RuleProduct rule gives an alternative formulation:
P(a b) = P(a | b) P(b) = P(b | a) P(a)
Joining them together, we can find-P(a | b) = P(b | a) P(a)
P(b)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 9
Application of Bayes’ RuleA doctor knows that the disease meningitis causes the patient to have a stiff neck is 50%Means probability of stiff neck given the probability of having meningitis P(s | m) = 0.5He also knows that in every 50000 patients, 1 may have meningitisMeans probability that a patient has meningitisP (m) = 1/50000He also knows that in every 20 patients, 1 may have stiff neckMeans probability that a patient has meningitisP (m) = 1/20Then, from Bayes’ ruleP(m | s) = P(s | m) P(m)
P(s)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 10
Application of Bayes’ RuleP(m | s) = P(s | m) P(m)
P(s)= 0.5 X (1/50000)
1/20= 0.0002
Means he can expect only 1 in 5000 patients with a stiff neck
to have meningitis
Rushdi Shams, Dept of CSE, KUET, Bangladesh 11
ReferencesArtificial Intelligence: A Modern Approach
(2nd Edition)by Russell and NorvigChapter 13