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Max Likelihood for BNs

Learning. Probabilistic Graphical Models. Parameter Estimation. Max Likelihood for BNs. MLE for Bayesian Networks. Parameters: Data instances: <x[m],y[m]>. X. Y. MLE for Bayesian Networks.  X. Parameters:. X.  Y|X. Y. Data d. MLE for Bayesian Networks.

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Max Likelihood for BNs

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  1. Learning Probabilistic Graphical Models Parameter Estimation Max Likelihoodfor BNs

  2. MLE for Bayesian Networks • Parameters: • Data instances: <x[m],y[m]> X Y

  3. MLE for Bayesian Networks X • Parameters: X Y|X Y Data d

  4. MLE for Bayesian Networks • Likelihood for Bayesian network  if Xi|Uiare disjoint, then MLE can be computed by maximizing each local likelihood separately

  5. MLE for Table CPDs

  6. MLE for Linear Gaussians

  7. Shared Parameters S’|S S(0) S(1) S(2) S(3)

  8. Shared Parameters S(0) S(1) S(2) S(3) O(1) O(2) O(3) S’|S O’|S’

  9. 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

  10. END END END

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