How to construct a set of factors that is a markov network

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Reference no: EM131851482

Problem

Suppose we are given a set of factors Φ = {φ₁, . . . , φ_K} over X = {X₁, . . . , X_n}. Our aim is to convert these factors into a pairwise Markov network by introducing new auxiliary variables Y = {Y₁, . . . , Y_k} so that Y_j denotes a joint assignment to Scope[φ_j]. Show how to construct a set of factors Φ' that is a pairwise Markov network over X ∪ Y such that P_Φ' (x) = P_Φ(x) for each assignment to X.

Reference no: EM131851482

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