Lecture 17:
More on exact
inference in Bayes
Nets
Prof. Julia Hockenmaier
[email protected]
http://cs.illinois.edu/fa11/cs440
CS440/ECE448: Intro to Artificial Intelligence
2
CS440/ECE448: Intro AI
Intelligence
Grade
SAT
Letter
Difficulty
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3
CS440/ECE448: Intro AI
Intelligence
Grade
SAT
Letter
Difficulty
What is the probability of getting a strong
letter if you are an intelligent student?
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Review: inference in Bayes Nets
What is the probability of getting a strong letter
if you are an intelligent student?
–
We want to compute the probability of a set of
query variables
X (= the letter)
given an event
e
(=
being intelligent)
–
An event = an assignment of values to a set of
evidence variables
E
(= intelligence)
4
CS440/ECE448: Intro AI
P
(
X
=
x

e
)
=
P
(
X
=
x

e
)
P
(
e
)
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Review: conditional probability
P
(
Y
)
can be computed by marginalization:
If we can compute
P
(
X,Y
)
, we can also
compute
P
(
X  Y
)
5
CS440/ECE448: Intro AI
P
(
X

Y
)
=
P
(
X
,
Y
)
P
(
Y
)
P
(
Y
=
y
)
=
P
(
X
=
x
,
Y
=
y
)
x
!
Computing inferences
in Bayes Nets
What is the probability of getting a strong
letter if you are an intelligent student?
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 Spring '08
 Levinson,S
 Conditional Probability, Burglary, Bayesian network, Intro AI

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