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Maximized Likelihood

Maximized Likelihood. Example 1. What is the maximized loglikelihood for the following structure? S: The parameters: P(A), P(B), P(C); d = 3 MLE : P(A=1)=1/2; P(B=1)=1/2; P(C=1)=3/4. Page 2. Example 1. The joint distribution represented by BN. Page 3. P(D| ).

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Maximized Likelihood

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  1. Maximized Likelihood

  2. Example 1 What is the maximized loglikelihood for the following structure? S: • The parameters: P(A), P(B), P(C); d = 3 • MLE : • P(A=1)=1/2; P(B=1)=1/2; P(C=1)=3/4 Page 2

  3. Example 1 The joint distribution represented by BN Page 3 P(D| ) • Maximized loglikelihood = log (3/16) + log (3/16) + log (3/16) + log (1/16) = - 2.42 - 2.42 - 2.42 - 4 = - 11.26

  4. Example 2 What is the BIC score for the following structure? S: • The parameters: P(A), P(B), P(C|B); d = 4 • MLE : • P(A=1)=1/2; P(B=1)=1/2; Page 4

  5. Example 2 The joint distribution represented by BN Page 5 P(D| ) • Maximized loglikelihood = log (1/4) + log (1/8) + log (1/4) + log (1/8) = - 2 - 3 - 2 - 3 - 4 = -10

  6. Page 6 Example 3 • What is the BIC score for the following structure? S: • The parameters: P(A), P(B), P(C|A, B); d = 7 • MLE : • P(A=1)=1/2;

  7. Page 7 Example 3 • The joint distribution represented by BN P(D| ) • Maximized Loglikelihood = log (1/4) + log (1/4) + log (1/4) + log (1/4) = - 2 - 2 - 2 - 2 = -8

  8. Page 8 Summary Structure Maximized Loglikelhood -11.26 -10 -8 • Maximized likelihood does not work • Lead to overfitting, i.e., very complexity model structure

  9. Page 10 Example (Cont’d) Structure loglikehihood Complexity BIC -11.26 3 -14.26 -10 4 -14 - 8 7 -15

  10. Example Page 11

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