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Unformatted text preview: Introduction to Probabilistic Graphical Models Problem Set #4 1 Probabilistic Graphical Models, Spring 2009 Problem Set #4 1. Consider the network shown in the figure, where we assume that all variables are binary, and that the F i variables in the second layer all have noisy or CPDs. Specifically, the CPD of F i is given by: P ( f i | Pa F i ) = (1- λ i, ) Y D j ∈ Pa F i (1- λ i,j ) d j where λ i,j is the noise parameter associated with parent D j of variable F i . This network architecture, called a BN2O network is characteristic of several medical diagnosis applica- tions, where the D i variables represent diseases (e.g., flu, pneumonia), and the F i variables represent medical findings (e.g., coughing, sneezing). Our general task is medical diagnosis: We obtain evidence concerning some of the findings, and we are interested in the resulting posterior probability over some subset of diseases....
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- Fall '07