383-Fall11-Lec21 - 1 CMPSCI 383 Nov 22, 2011 Learning...

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Unformatted text preview: 1 CMPSCI 383 Nov 22, 2011 Learning Probabilistic Models 2 Today s topics Full Bayesian Learning MAP approximation ML approximation ML parameter learning in Bayes nets Nave Bayes Model Linear Gaussian Model Bayesian parameter learning Beta family of distributions Conjugate families Latent variables Expectation Maximization (EM) algorithm 3 Full Bayesian Learning 3 Full Bayesian Learning 4 Example 5 Posterior Probabilities of the Hypotheses P ( h i | d ) = P ( d | h i ) P ( h i ) = P ( d j | h i ) j P ( h i ) prior distribution : 0.1,0.2,0.4,0.2,0.1 all limes selected 6 Prediction Probability 7 MAP approximation 8 ML approximation 9 ML parameter learning in Bayes nets 10 Multiple parameters 11 Multiple parameters contd. 12 Nave Bayes Model C X 1 X n X 2 class label Attributes: independent given C P (C | x 1 , x 2 , K , x n ) = P ( C ) P ( x i | C ) i C NB = argmax C lables P (C | x 1 , x 2 , K , x n ) = argmax P ( C ) P ( x i | C ) i Nave Bayes Classifer: 13...
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383-Fall11-Lec21 - 1 CMPSCI 383 Nov 22, 2011 Learning...

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