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**Unformatted text preview: **Machine Learning Srihari 1 From Distributions to Graphs Sargur Srihari [email protected] Machine Learning Srihari Topics • Bayesian Network • Semantics of Bayesian Networks – Minimal I-Maps – Perfect Maps • Finding Perfect Maps – Identifying the undirected skeleton – Identifying immoralities – Representing equivalence classes – I-Equivalence • Class PDAG • Summary of Bayesian Networks 2 Machine Learning Srihari Distribution represented by a Graph • Bayesian network is specified by a directed graph annotated with a set of conditional probability distributions P(X i |paX i ): local probability models • Network and local CPDs define global distribution P through chain rule 3 P ( D , I , G , S , L ) P ( D , I , G , S , L ) = P ( D ) P ( I ) P ( G | D , I ) P ( S | I ) P ( L | G ) Machine Learning Srihari Graph specifies Independencies • If distribution P factorizes over graph G – We can derive a rich set of independence assertions that hold for P by examining G • G reveals the structure of the distribution – We can test for independencies in P by constructing a graph G that represents P and testing d-separation in G 4 P ( D , I , G ,...

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