SP11 cs188 lecture 16 -- bayes nets IV 6PP

Sp11 cs188 lecture 16 bayes nets iv 6pp

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online