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Unformatted text preview: CS228 Problem Set #4 1 CS 228, Winter 2008 Problem Set #4 1. Parameter Estimation in Template-Based Models [20 points] In class, we talked about parameter learning in the case of partially observed data for general Bayesian networks. Here, we apply these methods to the special case of plate models. Consider the plate model in Figure 1 that has two plates, P 1 and P 2, with M and N copies, respectively. Let X be the variables that lie only in P 1, let Y be the variables that lie only in P 2, and let Z be the variables that lie in both plates. Each variable in Z must either have parents in both X and Y , have parents in Z , or both these must be true. (For a concrete example, see Figure 6.6 in the book.) Assume all variables are binary variables. Figure 1: Plate Model (a) [10 points] Suppose you are given the plate model as above, and a data set D where each training sample is a full assignment to all copies of the variables in X , all copies of the variables in Y , and all copies of the variables in Z . Let X denote the parameter vector for the CPDs of X , and similarly for Y and Z . Thus, for example, for a variable X i X , we have a parameter x i | u for each assignment x i to X i and u to Pa X i (note that the parents of X i must lie in P 1 and therefore be a subset of X )....
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- Winter '09