SP11 cs188 lecture 16 -- bayes nets IV 6PP

4 cold rain 06 24 25 4 example traffic domain random

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Unformatted text preview: Any assigned X or Y is a dimension missing (selected) from the array   Single conditional: P(Y | x)   Entries P(y | x) for fixed x, all y   Sums to 1 T W P cold sun 0.4 cold rain 0.6 24 25 4 Example: Traffic Domain   Random Variables R   R: Raining   T: Traffic   L: Late for class! Variable Elimination Outline   Track objects called factors   Initial factors are local CPTs (one per node) T +r  ­r 0.1 0.9 +t  ­t +t  ­t +l  ­l +l  ­l 0.3 0.7 0.1 0.9 +r  ­r 0.8 0.2 0.1 0.9 +t +t  ­t  ­t L +r +r  ­r  ­r +r  ­r 26 T T +r +t 0.08 +r  ­t 0.02  ­r +t 0.09  ­r  ­t 0.81 R,T   Computation for each entry: pointwise products 28 Example: Multiple Joins R, T +t  ­t +t  ­t 0.08 0.02 0.09 0.81 L +t +t  ­t  ­t +l  ­l +l  ­l 0.3 0.7 0.1 0.9 Join T +r +r +r +r  ­r  ­r  ­r  ­r +t +t  ­t  ­t +t +t  ­t  ­t +l  ­l +l  ­l +l  ­l +l  ­l +l  ­l +l  ­l 0.3 0.7 0.1 0.9 , the initial factors are +r +r  ­r  ­r +t  ­t +t  ­t 0.8 0.2 0.1 0.9 +t  ­t +l +l 0.3 0.1 27 +r  ­r 0.1 0.9 L +r +r  ­r  ­r +t  ­t +t  ­t 0.8 0.2 0.1 0.9 +l  ­l +l  ­l 0.3 0.7 0.1 0.9 Join R +r +r  ­r  ­r +t +t  ­t  ­t +t  ­t +t  ­t +l  ­l +l  ­l 0.08 0.02 0.09 0.81 0.3 0.7 0.1 0.9 R, T L 30 Operation 2: Eliminate   Second basic operation: marginalization   Take a factor and sum out a variable R, T, L +r +r  ­r  ­r 0.1 0.9 +t +t  ­t  ­t R 0.8 0.2 0.1 0.9 +t +t  ­t  ­t   VE: Alternately join factors and eliminate variables R   Example: Join on R +t  ­t +t  ­t 0.8 0.2 0.1 0.9 Example: Multiple Joins   Just like a database join   Get all factors over the joinin...
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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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