CSE 150 Lecture Notes - Lecture 7: Data Set, Maximum Likelihood Estimation, Polytree
25 Apr 2018
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P(x|e + x ) = u" p(x|u" = u") i = 1 to n p(u i = u i |e ui \ x ) Note: no cycles! b/c polytree has no loops. Linear in size of cpts (# of rows in cpt) b/c we must sum over parents , potentially at each node! Idea: turn loopy bn into polytree by clustering certain nodes . Node s takes on 2 3 values. S 1 | s 2 | s 3 | s | p(s|d = 0) | p(s|d = 1) Polytree alg. scales linearly in # of nodes and size of cpts grows exponentially w/ # nodes clustered into each mega-node . How to choose optimal clustering of nodes that leads to most efficient inference via polytree alg. Bn = dag + cpts: not always known or available from experts. Choose ( estimate") the model (bn = dag + cpt) to maximize p model (observed data)
