lecture 18 - CS 188: Artificial Intelligence Spring 2010...

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1 CS 188: Artificial Intelligence Spring 2010 Lecture 18: Bayes Nets V 3/30/2010 Pieter Abbeel – UC Berkeley Many slides over this course adapted from Dan Klein, Stuart Russell, Andrew Moore Announcements s Midterms s In glookup s Assignments s W5 due Thursday s W6 going out Thursday s Midterm course evaluations in your email soon 2
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2 Outline s Bayes net refresher: s Representation s Inference s Enumeration s Variable elimination s Approximate inference through sampling s Value of information 3 Bayes’ Net Semantics s A set of nodes, one per variable X s A directed, acyclic graph s A conditional distribution for each node s A collection of distributions over X, one for each combination of parents’ values s CPT: conditional probability table s Description of a noisy “causal” process A 1 X A n A Bayes net = Topology (graph) + Local Conditional Probabilities 4
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3 Probabilities in BNs s For all joint distributions, we have (chain rule): s Bayes’ nets implicitly encode joint distributions s As a product of local conditional distributions s To see what probability a BN gives to a full assignment, multiply all the relevant conditionals together: s This lets us reconstruct any entry of the full joint s Not every BN can represent every joint distribution s The topology enforces certain conditional independencies 5 Inference by Enumeration s Given unlimited time, inference in BNs is easy s Recipe: s State the marginal probabilities you need s Figure out ALL the atomic probabilities you need s Calculate and combine them s Building the full joint table takes time and space exponential in the number of variables 7
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4 General Variable Elimination s Query: s Start with initial factors: s Local CPTs (but instantiated by evidence) s While there are still hidden variables (not Q or evidence):
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This note was uploaded on 04/21/2010 for the course EECS 188 taught by Professor Cs188 during the Spring '01 term at University of California, Berkeley.

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lecture 18 - CS 188: Artificial Intelligence Spring 2010...

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