SP11 cs188 lecture 16 -- bayes nets IV 6PP

Sp11 cs188 lecture 16 bayes nets iv 6pp

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Unformatted text preview: Announcements CS 188: Artificial Intelligence Spring 2011   Assignments   W4 out today --- this is your last written!!   Any assignments you have not picked up yet   In bin in 283 Soda [same room as for submission drop-off] Lecture 16: Bayes Nets IV – Inference 3/28/2011 Pieter Abbeel – UC Berkeley Many slides over this course adapted from Dan Klein, Stuart Russell, Andrew Moore 2 Bayes Net Semantics Probabilities in BNs   For all joint distributions, we have (chain rule): A1 An   A set of nodes, one per variable X   A directed, acyclic graph   A conditional distribution for each node   Bayes nets implicitly encode joint distributions X   As a product of local conditional distributions   To see what probability a BN gives to a full assignment, multiply all the relevant conditionals together:   A collection of distributions over X, one for each combination of parents values   CPT: conditional probability table   Description of a noisy causal process A Bayes net = Topology (graph) + Local Conditional Probabilities   This lets us reconstruct any entry of the full joint   Not every BN can represent every joint distribution 3   The topology enforces certain conditional independencies 4 Possible to have same full list of conditional independence assumptions for different BN graphs? All Conditional Independences   Given a Bayes net structure, can run dseparation to build a complete list of conditional independences that are necessarily true of the form   Yes!   Examples: Xi ⊥ Xj |{Xk1 , ..., Xkn } ⊥   This list determines the set of probability distributions that can be represented 5 6 1 Topology Limits Distributions Causality? Y Y X Z {X ⊥ Y, X ⊥ Z, Y ⊥ Z, ⊥ ⊥ ⊥   Given some graph ⊥ ⊥ ⊥ topology G, only certain X ⊥ Z | Y, X ⊥ Y | Z, Y ⊥ Z | X } X Z joint distributions can {X ⊥ Z | Y } Y ⊥ be encoded X Z   The graph structure guarantees certain Y (conditional) independences X Z   (There might be more {} independence)   Adding arcs increases Y Y Y the set of distributions, X Z X Z X Z but has several costs   Full conditioning can Y Y Y encode any distribution 8 X Z X Z X Z   When Bayes nets reflect the true causal patterns:   Often simpler (nodes have fewer parents)   Often easier to think about   Often easi...
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