Posted: November 9th, 2015
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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