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Understanding Bayesian Networks: D-separation and Inference Techniques

This recitation covers key concepts in Bayesian networks, focusing on D-separation and Bayesian inference. We explore the concept of active trails and how conditional independence is determined based on observed variables. Specific examples illustrate the implications of D-separation and how it affects the independence of variables. The presentation is enriched by insights from previous years’ lectures and the work of Prof. Andrew Moore on data mining. By the end of this session, participants will gain a deeper understanding of the structures and inferences in Bayesian networks.

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Understanding Bayesian Networks: D-separation and Inference Techniques

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Presentation Transcript

  1. Bayesian Networks 10701/15781Recitation April 1, 2008 Kyung-Ah Sohn Parts of the slides are from previous years’ recitation and lecture notes, and from Prof. Andrew Moore’s data mining tutorials.

  2. Outline • D-separation • Bayesian inference

  3. Active Trail • A path Xi1-Xi2-…-Xik is an active trail when variables Z {X1,…,Xn} are observed if for each consecutive triplet in the trail: • xi-1 xi  xi+1 and xi is not observed • xi-1 xi  xi+1 and xi is not observed • xi-1 xi  xi+1 and xi is not observed • xi-1 xi  xi+1 and xi is observed, or one of its descendents is observed

  4. Conditional Independence • Variables Xi and Xj are independent given Z {X1,…,Xn} if there is NO ACTIVE TRAIL between Xi and Xj when variables Z are observed

  5. Examples • Trail from A to B

  6. I<A,{}, B> • I<A, {H}, B> • I<A, {F,H,G}, K}> • I<A, {F,D}, K>

  7. Bayesian inference • P(S) • P(S|A)

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