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lec19 - Lecture 19: November 1, 10 Exam 1 regrading: pl...

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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 •R e v i e w – Intro to probability theory – Probability distribution/density function – Cumulative distribution function – Joint and conditional probability – Bayes’ theorem •T o d a y – 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
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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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USC CS574: Computer Vision, Fall 2010 Copyright 2010, by R. Nevatia 4 Some Examples •C o i n t o s s –P (H ) = 0.5 (assumes fair coin) –P (H , H ) = 0.25 – P(H|H) =0.5 (prob that second toss is head, given first head) • Picking balls from an urn, initially 3 red and 3 green balls P ( red ) = 0.5 – P(red|one_green_picked) = 3/5 P ( 2 nd red ^1 st green ) = P ( red|green ) *P ( green ) = 0.6*0.5 P ( one_red ^ one_green ) = P ( red|green ) *P ( green ) + P ( green|red ) *P ( red ) • Playing cards (poker) – Probability of flush (five cards of same color), straight (sequence), three of a kind, full house (triple and pair)
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This note was uploaded on 11/23/2010 for the course CS 574 taught by Professor Ramnevatia during the Fall '10 term at USC.

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lec19 - Lecture 19: November 1, 10 Exam 1 regrading: pl...

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