lecture 15

# lecture 15 - CS 188 Artificial Intelligence Spring 2010...

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1 CS 188: Artificial Intelligence Spring 2010 Lecture 15: Bayes’ Nets II – Independence 3/9/2010 Pieter Abbeel – UC Berkeley Many slides over the course adapted from Dan Klein, Stuart Russell, Andrew Moore Announcements s Current readings s Require login s Assignments s W4 due Thursday s Midterm s 3/18, 6-9pm, 0010 Evans --- no lecture on 3/18 s We will be posting practice midterms s One page note sheet, non-programmable calculators s Topics go through Thursday, not next Tuesday 2

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2 Outline s Thus far: Probability s Today: Bayes nets s Semantics s (Conditional) Independence 3 Probability recap s Conditional probability s Product rule s Chain rule s X, Y independent iff: s X and Y are conditionally independent given Z iff: 4
Bayes’ Nets: Big Picture s Two problems with using full joint distribution tables as our probabilistic models: s Unless there are only a few variables, the joint is WAY too big to represent explicitly s Hard to learn (estimate) anything empirically about more than a few variables at a time s Bayes’ nets: a technique for describing complex joint distributions (models) using simple, local distributions (conditional probabilities) s More properly called graphical models s We describe how variables locally interact s Local interactions chain together to give global, indirect interactions s For about 10 min, we’ll be vague about how these interactions are specified 5 Graphical Model Notation s Nodes: variables (with domains) s Can be assigned (observed) or unassigned (unobserved) s Arcs: interactions s Similar to CSP constraints s Indicate “direct influence” between variables s Formally: encode conditional

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lecture 15 - CS 188 Artificial Intelligence Spring 2010...

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