BayesClassify-L6-L7-L8

# BayesClassify-L6-L7-L8 - CSE572:DataMining Bayesian...

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1 CSE 572: Data Mining Bayesian Classifiers

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2 Review: Probability A random variable is a quantity that depends on the outcome of a random experiment Can be discrete or continuous Example: Discrete random variable Random experiment : Tossing a coin 4 times Random variable : Number of tails that turn up Continuous random variable Random experiment : Observing person taking a roller coaster ride Random variable : height of the observed person
3 Example: Discrete random variable  Random experiment: Tossing a coin 4 times Outcomes: HHHH,HHHT,HHTH,…,TTTT Random variable X: number of tails observed Event, E: observing at least 3 tails that turn up P(E) = 4/16 + 1/16 = 5/16 X 0 1 2 3 4 P(X) 1/16 4/16 6/16 4/16 1/16 Probability mass function, P(X) X P(X) 0 1 2 3 4

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4 Example: Continuous random variable X takes continuous values f(x): Probability density function P(80K < Salary < 120K) = Salary f(Salary) K K dX X f 120 80 ) (
5 Probability functions

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6 Bayes Theorem A probabilistic approach for solving classification problems Conditional Probability: Bayes theorem: ) ( ) ( ) | ( ) | ( X P Y P Y X P X Y P = ) ( ) , ( ) | ( ) ( ) , ( ) | ( Y P Y X P Y X P X P Y X P X Y P = =
7 Example of Bayes Theorem Given: A doctor knows that meningitis causes stiff neck 50% of the time The probability that a patient has meningitis is 1/50,000 The probability that a patient has stiff neck is 1/20 If a patient has stiff neck, what’s the probability he/ she has meningitis? 0002 . 0 20 / 1 50000 / 1 5 . 0 ) ( ) ( ) | ( ) | ( = × = = S P M P M S P S M P

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8 Using Bayes Theorem for Classification Consider each attribute and class label as random variables Given a record with attributes (X 1 , X 2 ,…, X d ) Goal is to predict class Y Specifically, we want to find the value of Y that maximizes P(Y| X 1 , X 2 ,…, X d ) Can we estimate P(Y| X 1 , X 2 ,…, X d ) directly from data?
9 Using Bayes Theorem for Classification Approach: Compute posterior probability P(Y | X 1 , X 2 , …, X d ) using the Bayes theorem Choose Y that maximizes P(Y | X 1 , X 2 , …, X d ) Equivalent to choosing value of Y that maximizes

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## This note was uploaded on 04/08/2010 for the course CS 420 taught by Professor Dawsonengler during the Spring '02 term at San Jose State University .

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BayesClassify-L6-L7-L8 - CSE572:DataMining Bayesian...

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