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Learning with Hidden Variables
CSci 5512: Artifcial Intelligence II
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View Full Document 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
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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View Full Document 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
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.
 Spring '08
 Staff
 Artificial Intelligence

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