CSE P573 Applications of Artificial Intelligence Bayesian Learning

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Presentation transcript:

CSE P573 Applications of Artificial Intelligence Bayesian Learning Henry Kautz Autumn 2004

Classify instance D as:

Naive Bayes Classifier Important special, simple of a Bayes optimal classifier, where hypothesis = classification all attributes are independent given the class class attrib. 1 attrib. 3 attrib. 2

Expectation-Maximization Consider learning a naïve Bayes classifier using unlabeled data. How can we estimate e.g. P(A|C)? Initialization: randomly assign numbers to P(C), P(A|C), P(B|C) repeat { E-step: Compute P(C|A,B): M-step: Re-compute maximum likelihood estimation of P(C), P(A|C), P(B|C) Calculate log likelihood of data } until (likelihood of data not improving)

Expectation-Maximization Initialization: randomly assign numbers to P(C), P(A|C), P(B|C).

Expectation-Maximization E-step: Compute P(C|A,B)

Expectation-Maximization M-step: Re-compute maximum likelihood estimation of P(C), P(A|C), P(B|C):

Expectation-Maximization Calculate log likelihood of data:

EM Demo