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Probabilistic Reasoning Basics: Bayesian Networks in Artificial Intelligence

This tutorial explores basics of probabilistic reasoning using Bayesian networks. Topics covered include conditional and joint probabilities, Bayes' Rule, Markov Chain Monte Carlo, Gibbs sampling, Markov blanket sampling, and examples of diagnosing issues with PowerPoint printing and medical conditions. Learn how to calculate posterior probabilities and make inferences using probabilistic models.

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Probabilistic Reasoning Basics: Bayesian Networks in Artificial Intelligence

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  1. CSE 592Applications of Artificial IntelligenceWinter 2003 Probabilistic Reasoning

  2. Basics Ache No Ache Cavity 0.04 0.06 0.01 0.89 No Cavity • Random variable Cavity: yes or no P(Cavity) = 0.1 • Conditional Probability P(A|B) P(Cavity | Toothache) = 0.8 • Joint Probability Distribution (# variables)(# values) numbers • Bayes Rule P(B|A) = P(A|B)P(B) / P(A) • (Conditional) Independence P(A|C) = P(A) P(A | P,C) = P(A | C)

  3. In-Class Exercise • In groups of 2 or 3, sketch the structure of Bayes net that would be useful for diagnosing printing problems with Powerpoint • How could the network be used by a Help wizard? • 15 minutes

  4. The Normalization Shortcut

  5. Markov Chain Monte Carlo CSE 592

  6. MCMC with Gibbs Sampling • Fix the values of observed variables • Set the values of all non-observed variables randomly • Perform a random walk through the space of complete variable assignments. On each move: • Pick a variable X • Calculate Pr(X=true | all other variables) • Set X to true with that probability • Repeat many times. Frequency with which any variable X is true is it’s posterior probability. • Converges to true posterior when frequencies stop changing significantly • stable distribution, mixing CSE 592

  7. Markov Blanket Sampling • How to calculate Pr(X=true | all other variables) ? • Recall: a variable is independent of all others given it’s Markov Blanket • parents • children • other parents of children • So problem becomes calculating Pr(X=true | MB(X)) • We solve this sub-problem exactly • Fortunately, it is easy to solve CSE 592

  8. Example A C X B CSE 592

  9. Example • Evidence: • S=true, B=true smoking heartdisease lungdisease shortnessof breath CSE 592

  10. Example 2 • Evidence: • S=true, B=true • Randomly setH=false, L=true smoking heartdisease lungdisease shortnessof breath CSE 592

  11. Example 3 • Sample H: • P(h|s,l,b)=P(h|s)P(b|h,l) • = (0.6)(0.9)=  0.54 • P(h|s,l,b)=P(h|s)P(b| h,l) • = (0.4)(0.7)=  0.28 • Normalize: 0.54/(0.54+0.28)=0.66 • Flip coin: H becomes true (maybe) smoking heartdisease lungdisease shortnessof breath CSE 592

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