USC
CS574: Computer Vision, Fall 2010
Copyright 2010, by R. Nevatia
1
Lecture 19: November 1, 10
•
Exam 1 regrading: pl submit by today
•
HW4, due today
•
Make up class, Friday, Nov 5, 9:30 to 10:50 am, Studio D
• Review
–
Intro to probability theory
–
Probability distribution/density function
–
Cumulative distribution function
–
Joint and conditional probability
– Bayes’ theorem
• Today
–
More on prob theory
–
Bayesian classifiers

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USC
CS574: Computer Vision, Fall 2010
Copyright 2010, by R. Nevatia
2
Joint Probability Distribution
•
Probability of two (or more) events occurring together
– say
P
(
X= x
i
and Y= y
j
)
, e.g. P
(
cavity, toothache
)
•
Full joint probability distribution
–
P
(
X, Y
), 2-D table giving probabilities for every combination of
values of
X
and
Y
–
Can compute
P
(
X
) by summing over all values of
Y
, e.g. in
above
P
(c
avity
)
= 0.1, P
(
toothache
)
= .05

USC
CS574: Computer Vision, Fall 2010
Copyright 2010, by R. Nevatia
3
Conditional Probability
•
Probability of a random variable may change if value of
another variable is given
e.g.
P
(
cavity|toothache
) = 0.8
–
Notation: P (a|b), prob of
a
given that all we know is
b
•
If we know
B
and also know
C,
then
P
(
A| B
C
)
•
Product rule:
–
P
(
A|B
)
= P
(
A
B
)
/ P
(
B
)
–
P
(
A
B
)
= P
(
A|B
)
*P
(
B
)
–
P
(
A
B
)
= P
(
B|A
)
*P
(
A
)
•
Conditional distribution
P
(
X|Y
) gives values of
P
(
X= x
i
,
Y= y
j
) for all possible values of
i
and
j
,
m x n
table

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