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

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Learning with Hidden Variables CSci 5512: Artificial 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
Example: Diagnostic Network Smoking Diet Exercise Symptom 1 Symptom 2 Symptom 3 (a) (b) HeartDisease Smoking Diet Exercise Symptom 1 Symptom 2 Symptom 3 2 2 2 54 6 6 6 2 2 2 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
The Mixture Model Learning Problem

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