SP11 cs188 lecture 15 -- bayes nets III 6PP

SP11 cs188 lecture 15 -- bayes nets III 6PP - Announcements...

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1 CS 188: Artificial Intelligence Spring 2011 Lecture 15: Bayes ` Nets III 3/16/2011 Pieter Abbeel – UC Berkeley Many slides over this course adapted from Dan Klein, Stuart Russell, Andrew Moore Announcements § Current readings § Require login § Midterm § This week’s section will discuss midterm solutions 2 Our Bayes ` Nets Status § We now know: § What is a Bayes ` net? § What joint distribution does a Bayes ` net encode? § Now: properties of that joint distribution (independence) § Key idea: conditional independence § Last class: assembled BNs using an intuitive notion of conditional independence as causality § Today: formalize these ideas § Main goal: answer queries about conditional independence and influence --- important to understand modeling assumptions § Next: how to compute posteriors quickly (inference) § Next-next: how to learn a Bayes net from data 3 Bayes ` Net Semantics § A set of nodes, one per variable X § A directed, acyclic graph § A conditional distribution for each node § A collection of distributions over X, one for each combination of parents ` values § CPT: conditional probability table § Description of a noisy l causal z process A 1 X A n A Bayes net = Topology (graph) + Local Conditional Probabilities 5 Example: Alarm Network B urglary E arthqk A larm J ohn calls M ary calls B P(B) +b 0.001 ¬ b 0.999 E P(E) +e 0.002 ¬ e 0.998 B E A P(A|B,E) +b +e +a 0.95 +b +e ¬ a 0.05 +b ¬ e +a 0.94 +b ¬ e ¬ a 0.06 ¬ b +e +a 0.29 ¬ b +e ¬ a 0.71 ¬ b ¬ e +a 0.001 ¬ b ¬ e ¬ a 0.999 A J P(J|A) +a +j 0.9 +a ¬ j 0.1 ¬ a +j 0.05 ¬ a ¬ j 0.95 A M P(M|A) +a +m 0.7 +a ¬ m 0.3 ¬ a +m 0.01 ¬ a ¬ m 0.99 Size of a Bayes ` Net § How big is a joint distribution over N Boolean variables? 2 N § How big is an N-node net if nodes have up to k parents? O(N * 2 k+1 ) § Both give you the power to calculate § BNs: Huge space savings! § Also easier to elicit local CPTs § Also turns out to be faster to answer queries (next lecture) 7
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2 Chain Rule à Bayes net § Chain rule: can always write any joint distribution as an incremental product of conditional distributions § Bayes nets: make conditional independence assumptions of the form: giving us: 8 P ( x i | x 1 ··· x i 1 )= P ( x i | parents ( X i ))
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SP11 cs188 lecture 15 -- bayes nets III 6PP - Announcements...

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