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lecture 17

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 square4 Assignments square4 W4 back today in lecture square4 Any assignments you have not picked up yet square4 In bin in 283 Soda [same room as for submission drop-off] square4 Midterm square4 3/18, 6-9pm, 0010 Evans --- no lecture on Thursday square4 We have posted practice midterms (and finals) square4 One note letter-size note sheet (two sides), non-programmable calculators [strongly encouraged to compose your own!] square4 Topics go through last Thursday square4 Section this week: midterm review 2

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2 Bayes’ Net Semantics square4 Let’s formalize the semantics of a Bayes’ net 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 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 4
3 Bayes Nets Representation Summary square4 Bayes nets compactly encode joint distributions square4 Guaranteed independencies of distributions can be deduced from BN graph structure square4 D-separation gives precise conditional independence guarantees from graph alone

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

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