SP11 cs188 lecture 16 -- bayes nets IV 6PP

Inspect its specific distribution 16 inference

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Unformatted text preview: ning Bayes Nets from Data   A Bayes net s joint distribution may have further (conditional) independence that is not detectable until you inspect its specific distribution 16 Inference   Inference: calculating some useful quantity from a joint probability distribution   Examples: 17 Inference by Enumeration B   Given unlimited time, inference in BNs is easy   Recipe: E   State the marginal probabilities you need   Figure out ALL the atomic probabilities you need   Calculate and combine them A   Posterior probability:   Example: J B E M   Most likely explanation: A 18 J M 19 3 Example: Enumeration Inference by Enumeration?   In this simple method, we only need the BN to synthesize the joint entries 20 Variable Elimination 21 Factor Zoo I   Why is inference by enumeration so slow?   You join up the whole joint distribution before you sum out the hidden variables   You end up repeating a lot of work! T   Entries P(x,y) for all x, y   Sums to 1 W P hot   Joint distribution: P(X,Y) sun 0.4   A slice of the joint distribution   Entries P(x,y) for fixed x, all y   Sums to P(x) 22 Factor Zoo II   Family of conditionals: P(X |Y)   Multiple conditionals   Entries P(x | y) for all x, y   Sums to |Y| 0.1 sun 0.2 rain 0.3   Selected joint: P(x,Y)   Called Variable Elimination   Still NP-hard, but usually much faster than inference by enumeration   We ll need some new notation to define VE rain cold   Idea: interleave joining and marginalizing! hot cold T W P cold sun 0.2 cold rain 0.3   Number of capitals = dimensionality of the table 23 Factor Zoo III T W sun   Specified family: P(y | X) P hot 0.8 hot rain 0.2 cold sun 0.4 cold rain   Entries P(y | x) for fixed y, but for all x   Sums to … who knows! T W P hot rain 0.2 cold rain 0.6 0.6   In general, when we write P(Y1 … YN | X1 … XM)   It is a factor, a multi-dimensional array   Its values are all P(y1 … yN | x1 … xM) ...
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This note was uploaded on 08/26/2011 for the course CS 188 taught by Professor Staff during the Spring '08 term at Berkeley.

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