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lecture 18

# 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 square4 Midterms square4 In glookup square4 Assignments square4 W5 due Thursday square4 W6 going out Thursday square4 Midterm course evaluations in your email soon 2

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2 Outline square4 Bayes net refresher: square4 Representation square4 Inference square4 Enumeration square4 Variable elimination square4 Approximate inference through sampling square4 Value of information 3 Bayes’ Net Semantics square4 A set of nodes, one per variable X square4 A directed, acyclic graph square4 A conditional distribution for each node square4 A collection of distributions over X, one for each combination of parents’ values square4 CPT: conditional probability table square4 Description of a noisy “causal” process A 1 X A n A Bayes net = Topology (graph) + Local Conditional Probabilities 4
3 Probabilities in BNs square4 For all joint distributions, we have (chain rule): square4 Bayes’ nets implicitly encode joint distributions square4 As a product of local conditional distributions square4 To see what probability a BN gives to a full assignment, multiply all the relevant conditionals together: square4 This lets us reconstruct any entry of the full joint square4 Not every BN can represent every joint distribution square4 The topology enforces certain conditional independencies 5 Inference by Enumeration square4 Given unlimited time, inference in BNs is easy square4 Recipe: square4 State the marginal probabilities you need square4 Figure out ALL the atomic probabilities you need square4 Calculate and combine them square4 Building the full joint table takes time and space exponential in the number of variables 7

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4 General Variable Elimination square4 Query: square4
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lecture 18 - CS 188 Artificial Intelligence Spring 2010...

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