Posted: November 9th, 2015

Introduction to Graphical Models

Introduction to Graphical Models

Consider the Bayesian network in Figure ??. (a) Apply variable elimination to compute the marginal

probabilities of: (1) Variable F: p(F) (2) Variable G: p(G) (3) The variables C and G jointly: p(C,G). For

each part, report the elimination order used, along with the schematic computation of each bucket (e.g.,

which functions are collected together at each step, what function is produced, and their scopes). Also, what

is the largest scope of any of the produced functions (the induced width of the computation)? You may use

pyGM or any other software tool to perform the actual calculations, or do them manually if you prefer. (b)

Suppose that we observe evidence D = 0,C = 1. Apply variable elimination to compute the probability of the

evidence, p(D = 0,C = 1). Again, report the operations performed as well as the result. What is the largest

function constructed in performing this computation? (Note: it should be more efficient than directly

computing the marginal probability over (C,D) for all values of C,D.) (c) Apply max variable elimination to

find the most probable configuration of the variables given evidence F = 0. What is the most likely

configuration? Again, what was the largest function constructed? I would like to start the bid at $60.

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