SP11 cs188 lecture 14 -- bayes nets II 6PP

SP11 cs188 lecture 14 -- bayes nets II 6PP - Announcements...

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1 CS 188: Artificial Intelligence Spring 2011 Lecture 14: Bayes ` Nets II – Independence 3/9/2011 Pieter Abbeel – UC Berkeley Many slides over the course adapted from Dan Klein, Stuart Russell, Andrew Moore Announcements § Current readings § Require login § Assignments § W3 due Friday § Optional Practice Midterm due Friday § Next week § Monday lecture = midterm review § Tuesday: midterm 5-8pm, see course webpage for specifics 2 Outline § Thus far: Probability § Today: § Independence § Bayes nets § Semantics § (Conditional) Independence 3 Probabilistic Models § Models describe how (a portion of) the world works § Models are always simplifications § May not account for every variable § May not account for all interactions between variables § l All models are wrong; but some are useful. z – George E. P. Box § What do we do with probabilistic models? § We (or our agents) need to reason about unknown variables, given evidence § Example: explanation (diagnostic reasoning) § Example: prediction (causal reasoning) § Example: value of information 4 Probabilistic Models § For n variables with domain sizes d, joint distribution table with d n -1 free parameters [recall probabilities sum to one] § Size of representation if we use the chain rule Concretely, counting the number of free parameters accounting for that we know probabilities sum to one: (d-1) + d(d-1) + d 2 (d-1) + + d n-1 (d-1) = (d n -1)/(d-1) (d-1) = d n - 1 [why do both representations have the same number of free parameters?] 5 Independence § Two variables are independent if: § This says that their joint distribution factors into a product two simpler distributions § Another form: § We write: § Independence is a simplifying modeling assumption § Empirical joint distributions: at best l close z to independent § What could we assume for {Weather, Traffic, Cavity, Toothache}?
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SP11 cs188 lecture 14 -- bayes nets II 6PP - Announcements...

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