Probabilistic logic

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Probabilistic logic

  1. 1. Rushdi Shams, Dept of CSE, KUET, Bangladesh 1 Knowledge Representation Probabilistic Logic Artificial Intelligence Version 2.0
  2. 2. Rushdi Shams, Dept of CSE, KUET, Bangladesh 2 Conditional Probability  Definition 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)
  3. 3. Rushdi Shams, Dept of CSE, KUET, Bangladesh 3 Inference with Probability
  4. 4. Rushdi Shams, Dept of CSE, KUET, Bangladesh 4 Inference in Probability  P(toothache) = 0.108 + 0.012 + 0.016 + 0.064 = 0.2
  5. 5. Rushdi Shams, Dept of CSE, KUET, Bangladesh 5 Inference in Probability  P(cavity V toothache) = 0.108 + 0.012 + 0.072 + .008 + 0.016 + 0.064 = 0.28
  6. 6. Rushdi Shams, Dept of CSE, KUET, Bangladesh 6 Inference in Probability  Can also compute conditional probabilities:
  7. 7. Rushdi Shams, Dept of CSE, KUET, Bangladesh 7 Inference in Probability  Can also compute conditional probabilities:
  8. 8. Rushdi Shams, Dept of CSE, KUET, Bangladesh 8 Baye’s Rule  Product 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)
  9. 9. Rushdi Shams, Dept of CSE, KUET, Bangladesh 9 Application of Bayes’ Rule A 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) = 0.5 He also knows that in every 50000 patients, 1 may have meningitis Means probability that a patient has meningitis P (m) = 1/50000 He also knows that in every 20 patients, 1 may have stiff neck Means probability that a patient has meningitis P (m) = 1/20 Then, from Bayes’ rule P(m | s) = P(s | m) P(m) P(s)
  10. 10. Rushdi Shams, Dept of CSE, KUET, Bangladesh 10 Application of Bayes’ Rule P(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
  11. 11. Rushdi Shams, Dept of CSE, KUET, Bangladesh 11 References  Artificial Intelligence: A Modern Approach (2nd Edition) by Russell and Norvig Chapter 13

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