Max Likelihood for BNs
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Daphne Koller Parameter Estimation Max Likelihood for BNs Probabilistic Graphical Models Learning
description
Learning. Probabilistic Graphical Models. Parameter Estimation. Max Likelihood for BNs. MLE for Bayesian Networks. Parameters: Data instances: . X. Y. MLE for Bayesian Networks. X. Parameters:. X. Y|X. Y. Data d. MLE for Bayesian Networks. - PowerPoint PPT Presentation
Transcript of Max Likelihood for BNs
Daphne Koller
Parameter Estimation
Max Likelihoodfor BNs
ProbabilisticGraphicalModels
Learning
Daphne Koller
MLE for Bayesian Networks• Parameters:
• Data instances: <x[m],y[m]> X
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Daphne Koller
MLE for Bayesian Networks• Parameters:
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Daphne Koller
MLE for Bayesian Networks• Likelihood for Bayesian network
if Xi|Ui are disjoint, then MLE can be computed by
maximizing each local likelihood separately
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Daphne Koller
MLE for Table CPDs
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Daphne Koller
MLE for Linear Gaussians
Daphne Koller
Shared ParametersS(1)S(0) S(2) S(3)
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Daphne Koller
Shared Parameters
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Daphne Koller
Summary• For BN with disjoint sets of parameters in
CPDs, likelihood decomposes as product of local likelihood functions, one per variable
• For table CPDs, local likelihood further decomposes as product of likelihood for multinomials, one for each parent combination
• For networks with shared CPDs, sufficient statistics accumulate over all uses of CPD
Daphne Koller
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