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lec19

# lec19 - Lecture 19 November 1 10 Exam 1 regrading pl submit...

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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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