lecture 17 - CS 188: Artificial Intelligence Spring 2010...

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1 CS 188: Artificial Intelligence Spring 2010 Lecture 17: Bayes’ Nets IV – Inference 3/16/2010 Pieter Abbeel – UC Berkeley Many slides over this course adapted from Dan Klein, Stuart Russell, Andrew Moore Announcements s Assignments s W4 back today in lecture s Any assignments you have not picked up yet s In bin in 283 Soda [same room as for submission drop-off] s Midterm s 3/18, 6-9pm, 0010 Evans --- no lecture on Thursday s We have posted practice midterms (and finals) s One note letter-size note sheet (two sides), non-programmable calculators [strongly encouraged to compose your own!] s Topics go through last Thursday s Section this week: midterm review 2
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2 Bayes’ Net Semantics s Let’s formalize the semantics of a Bayes’ net 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 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 4
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3 Bayes Nets Representation Summary s Bayes nets compactly encode joint distributions s Guaranteed independencies of distributions can be deduced from BN graph structure s D-separation gives precise conditional independence guarantees from graph alone s A Bayes’ net’s joint distribution may have further (conditional) independence that is not detectable
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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 17 - CS 188: Artificial Intelligence Spring 2010...

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