SP11 cs188 lecture 13 -- bayes nets 6PP

SP11 cs188 lecture 13 -- bayes nets 6PP - Announcements CS...

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1 CS 188: Artificial Intelligence Spring 2011 Lecture 13: Bayes ` Nets 3/7/2011 Pieter Abbeel – UC Berkeley Many slides throughout the course adapted from Dan Klein, Stuart Russell, Andrew Moore Announcements § Assignments § P3 was due at 4:59pm today § W3 (probability) is out and due on Friday at 5:29pm (283 Soda) § Practice Midterm (optional) is out § 1% EC on midterm for submission, 1% EC on midterm for self-corrected re-submission § Due Friday at 5:29pm (283 Soda) § Solution sets for W3 and Practice Midterm available on Friday at 5:30pm at 283 Soda § Midterm § 3/15, 5-8pm, 155 Dwinelle § Midterm review lecture on 3/14 2 Part II: Probabilistic Reasoning § Probability § Random Variables § Joint and Marginal Distributions § Conditional Distribution § Inference by Enumeration § Product Rule, Chain Rule, Bayes ` Rule § Independence § Distributions over LARGE Numbers of Random Variables § Representation § Inference 3 Random Variables § A random variable is some aspect of the world about which we (may) have uncertainty § R = Is it raining? § D = How long will it take to drive to work? § L = Where am I? § We denote random variables with capital letters § Like variables in a CSP, random variables have domains § R in {true, false} (sometimes write as {+r, ¬ r}) § D in [0, ) § L in possible locations, maybe {(0,0), (0,1), } 4 Probability Distributions § Unobserved random variables have distributions § A distribution is a TABLE of probabilities of values § A probability (lower case value) is a single number § Must have: 5 T P warm 0.5 cold 0.5 W P sun 0.6 rain 0.1 fog 0.3 meteor 0.0 Joint Distributions § A joint distribution over a set of random variables: specifies a real number for each assignment (or outcome ): § Size of distribution if n variables with domain sizes d? § Must obey: § For all but the smallest distributions, impractical to write out T W P hot sun 0.4 hot rain 0.1 cold sun 0.2 cold rain 0.3 6

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2 Probabilistic Models § A probabilistic model is a joint distribution over a set of random variables § Probabilistic models: § (Random) variables with domains Assignments are called outcomes § Joint distributions: say whether assignments (outcomes) are likely § Normalized: sum to 1.0 § Ideally: only certain variables directly interact § Constraint satisfaction probs: § Variables with domains § Constraints: state whether assignments are possible § Ideally: only certain variables directly interact T W P hot sun 0.4 hot rain 0.1 cold sun 0.2 cold rain 0.3 T W P hot sun T hot rain F cold sun F cold rain T 7 Distribution over T,W Constraint over T,W Events § An event is a set E of outcomes § From a joint distribution, we can calculate the probability of any event § Probability that it ` s hot AND sunny? § Probability that it
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SP11 cs188 lecture 13 -- bayes nets 6PP - Announcements CS...

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