lecture10 - Data Mining CS57300 Purdue University Naive...

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Data Mining CS57300 Purdue University September 28, 2010
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Naive Bayes classifier (cont) P ( C | X ) = P ( X | C ) P ( C ) P ( X ) m i =1 P ( X i | C ) P ( C )
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NBC learning Estimate prior P(C) and conditional probability distributions P(X i | C) independently w/MLE • P(C)=9/14 P(I=high|C=yes)=2/9 P(I=med|C=yes)=4/9 P(I=low|C=yes)=3/9 etc. age income student credit_rating buys_computer <=30 high no fair no <=30 high no excellent no 31…40 high no fair yes >40 medium no fair yes >40 low yes fair yes >40 low yes excellent no 31…40 low yes excellent yes <=30 medium no fair no <=30 low yes fair yes >40 medium yes fair yes <=30 medium yes excellent yes 31…40 medium no excellent yes 31…40 high yes fair yes >40 medium no excellent no
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Learning CPTs from examples 0 13 2 False 17 13 10 True High Medium Low f( x ) X 1 P[ X 1 = Low | f(x) = True] = 10 (10 + 13 + 17) P[ F(x) = False] = (2 + 13) (2 + 13 + 10 + 13 + 17)
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Zero counts are a problem If an attribute value does not occur in training example, we assign zero probability to that value How does that affect the conditional probability P[ F(x) | x ] ? It equals 0!!! Why is this a problem? Adjust for zero counts by “smoothing” probability estimates
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Add uniform prior Smoothing: Laplace correction 0 13 2 False 17 13 10 True High Medium Low f( x ) X 1 P[ X 1 = High | f(x) = False] = 0 (2 + 13 + 0) 0 + 1 + 0) + 3
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Is assuming independence a problem? What is the effect on probability estimates? Over-counting evidence, leads to overly confident probability estimate What is the effect on classification? Less clear… For a given input x , suppose f( x ) = True Naïve Bayes will correctly classify if P[ F( x ) = True | x ] > 0.5
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Naive Bayes classifier
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