CS 1571 Introduction to AI
Lecture 24
Bayesian belief networks
Milos Hauskrecht
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
Lecture 24
Bayesian belief networks
Milos Hauskrecht
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
