CS 1571 Introduction to AI
Lecture 25
Bayesian belief networks
Inference
Milos Hauskrecht
5329 Sennott Square
CS 1571 Intro to AI M. Hauskrecht
Administration
• Homework assignment 10 is out and due on Wednesday
• Final exam:
– December 11, 2006
– 12:00-1:50pm, 5129 Sennott Square
CS 1571 Intro to AI M. Hauskrecht
1
, 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
Bayesian belief network.
2. Local conditional distributions
• relate variables and their parents
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
2
, Bayesian belief network.
P(B) P(E)
T F T F
Burglary 0.001 0.999 Earthquake 0.002 0.998
P(A|B,E)
B E T F
T T 0.95 0.05
Alarm T F 0.94 0.06
F T 0.29 0.71
F F 0.001 0.999
P(J|A) P(M|A)
A T F A T F
JohnCalls T 0.90 0.1 MaryCalls T 0.7 0.3
F 0.05 0.95 F 0.01 0.99
CS 1571 Intro to AI M. Hauskrecht
Full joint distribution in BBNs
Full joint distribution is defined in terms of local conditional
distributions (obtained via the chain rule):
P ( X 1 , X 2 ,.., X n ) = ∏ P( X
i =1,.. n
i | pa ( X i ))
B E
Example:
Assume the following assignment A
of values to random variables
B = T, E = T, A = T, J = T, M = F J M
Then its probability is:
P(B = T, E = T, A = T, J = T, M = F) =
P(B = T)P(E = T)P(A = T | B = T, E = T)P(J = T | A = T)P(M = F | A = T)
CS 1571 Intro to AI M. Hauskrecht
3
Lecture 25
Bayesian belief networks
Inference
Milos Hauskrecht
5329 Sennott Square
CS 1571 Intro to AI M. Hauskrecht
Administration
• Homework assignment 10 is out and due on Wednesday
• Final exam:
– December 11, 2006
– 12:00-1:50pm, 5129 Sennott Square
CS 1571 Intro to AI M. Hauskrecht
1
, 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
Bayesian belief network.
2. Local conditional distributions
• relate variables and their parents
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
2
, Bayesian belief network.
P(B) P(E)
T F T F
Burglary 0.001 0.999 Earthquake 0.002 0.998
P(A|B,E)
B E T F
T T 0.95 0.05
Alarm T F 0.94 0.06
F T 0.29 0.71
F F 0.001 0.999
P(J|A) P(M|A)
A T F A T F
JohnCalls T 0.90 0.1 MaryCalls T 0.7 0.3
F 0.05 0.95 F 0.01 0.99
CS 1571 Intro to AI M. Hauskrecht
Full joint distribution in BBNs
Full joint distribution is defined in terms of local conditional
distributions (obtained via the chain rule):
P ( X 1 , X 2 ,.., X n ) = ∏ P( X
i =1,.. n
i | pa ( X i ))
B E
Example:
Assume the following assignment A
of values to random variables
B = T, E = T, A = T, J = T, M = F J M
Then its probability is:
P(B = T, E = T, A = T, J = T, M = F) =
P(B = T)P(E = T)P(A = T | B = T, E = T)P(J = T | A = T)P(M = F | A = T)
CS 1571 Intro to AI M. Hauskrecht
3
