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Summary Bayesian belief networks

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Bayesian belief networks

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CS 1571 Introduction to AI
Lecture 24




Bayesian belief networks


Milos Hauskrecht
milos@cs.pitt.edu
5329 Sennott Square



CS 1571 Intro to AI M. Hauskrecht




Administration

• Homework assignment 10 is out and due next week
• Final exam:
– December 11, 2006
– 12:00-1:50pm, 5129 Sennott Square




CS 1571 Intro to AI M. Hauskrecht




1

, Modeling uncertainty with probabilities
• Knowledge based system era (70s – early 80’s)
– Extensional non-probabilistic models
– Solve the space, time and acquisition bottlenecks in
probability-based models
– froze the development and advancement of KB systems
and contributed to the slow-down of AI in 80s in general

• Breakthrough (late 80s, beginning of 90s)
– Bayesian belief networks
• Give solutions to the space, acquisition bottlenecks
• Partial solutions for time complexities
• Bayesian belief network


CS 1571 Intro to AI M. Hauskrecht




Bayesian belief networks (BBNs)
Bayesian belief networks.
• Represent the full joint distribution over the variables more
compactly with a smaller number of parameters.
• Take advantage of conditional and marginal independences
among random variables

• A and B are independent
P ( A, B ) = P ( A ) P ( B )
• A and B are conditionally independent given C

P ( A, B | C ) = P ( A | C ) P ( B | C )
P( A | C , B) = P( A | C )

CS 1571 Intro to AI M. Hauskrecht




2

, Alarm system example.
• Assume your house has an alarm system against burglary.
You live in the seismically active area and the alarm system
can get occasionally set off by an earthquake. You have two
neighbors, Mary and John, who do not know each other. If
they hear the alarm they call you, but this is not guaranteed.
• We want to represent the probability distribution of events:
– Burglary, Earthquake, Alarm, Mary calls and John calls

Causal relations Burglary Earthquake




Alarm




JohnCalls MaryCalls

CS 1571 Intro to AI M. Hauskrecht




Bayesian belief network.
1. Directed acyclic graph
• Nodes = random variables
Burglary, Earthquake, Alarm, Mary calls and John calls
• Links = direct (causal) dependencies between variables.
The chance of Alarm is influenced by Earthquake, The
chance of John calling is affected by the Alarm
Burglary P(B) Earthquake P(E)




Alarm P(A|B,E)


P(J|A) P(M|A)

JohnCalls MaryCalls

CS 1571 Intro to AI M. Hauskrecht




3

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