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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 dropoff] 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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 Spring '08
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 Artificial Intelligence

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