em1 - Learning with Hidden Variables CSci 5512: Artificial...

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Learning with Hidden Variables CSci 5512: Artifcial Intelligence II
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Hidden Variables Real world problem have hidden variables No training data available on hidden variables Model cannot be built without training data Inference cannot be done without model How to learn models with hidden variables Instructor: Arindam Banerjee Learning with Hidden Variables
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Example: Diagnostic Network Smoking Diet Exercise Symptom 1 Symptom 2 Symptom 3 (a) (b) HeartDisease Smoking Diet Exercise Symptom 1 Symptom 2 Symptom 3 222 54 666 54 162 486 Each node has 3 values: none, moderate, severe Model with hidden variable has 78 parameters Model without hidden variable has 708 parameters Hidden variables allow simpler models Instructor: Arindam Banerjee Learning with Hidden Variables
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Probabilistic Mixture Models Consider a mixture model of the form p ( x | π, θ ) = k X h =1 π h p ( x | θ h ) p ( x | θ h ) is the h th mixing component π h is the mixing weight Mixing component p ( x | θ h ) is a density function with parameter θ h Example: Gaussians, Multinomials, Bernoulli Each component corresponds to one cluster Mixing weight Forms a probability distribution over components, h π h = 1 Relative proportion of each cluster Instructor: Arindam Banerjee Learning with Hidden Variables
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The Mixture Model Learning Problem Given: Data
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This note was uploaded on 02/07/2012 for the course CSCI 5512 taught by Professor Staff during the Spring '08 term at Minnesota.

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em1 - Learning with Hidden Variables CSci 5512: Artificial...

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