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Bayesian Networks

Bayesian Networks. 10701 /15781 Recitation 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. Outline. D-separation Bayesian inference. Active Trail.

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Bayesian Networks

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  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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