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383-Fall11-Lec21 - 1 CMPSCI 383 Learning Probabilistic...

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Unformatted text preview: 1 CMPSCI 383 Nov 22, 2011 Learning Probabilistic Models 2 Today ʼ s topics • Full Bayesian Learning • MAP approximation • ML approximation • ML parameter learning in Bayes nets • Naïve 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 ) = α P ( d | h i ) P ( h i ) = α 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 Naïve Bayes Model C X 1 X n X 2 class label Attributes: independent given C P (C | x 1 , x 2 , K , x n ) = α P ( C ) P ( x i | C ) i ∏ C NB = argmax C ∈ lables P (C | x 1 , x 2 , K , x n ) = argmax α P ( C ) P ( x i | C ) i ∏ Naïve Bayes Classifer: 13...
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383-Fall11-Lec21 - 1 CMPSCI 383 Learning Probabilistic...

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