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Linear Models for Classification 2 Chap. 4 of PRML

2012-6-3. Pattern Recognition and Machine Learning. 2. ??. ???? vs. ??????????(Probabilistic Discriminative Models)??????(Laplace Approximation)???Logistic??(Bayesian Logistic Regression). 2012-6-3. Pattern Recognition and Machine Learning. 3. ????. ??????,????????:???(Inference step);Determi

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Linear Models for Classification 2 Chap. 4 of PRML

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    1. Linear Models for Classification (2) (Chap. 4 of PRML) Presented by: Zhiyang Wang 2009-06

    2. 2012-6-3 Pattern Recognition and Machine Learning 2 ?? ???? vs. ???? ??????(Probabilistic Discriminative Models) ??????(Laplace Approximation) ???Logistic??(Bayesian Logistic Regression)

    3. 2012-6-3 Pattern Recognition and Machine Learning 3 ???? ??????,????????: ???(Inference step); Determine either or . ???(Decision step): For given x, determine optimal t.

    4. 2012-6-3 Pattern Recognition and Machine Learning 4 ???? vs. ???? ????: Model Use Bayes theorem ????: Model directly

    5. 2012-6-3 Pattern Recognition and Machine Learning 5 ?????? ???? ????????? ,????????? ????? ??????? ???????(?????????? ??????????) ???????(basis functions)

    6. 2012-6-3 Pattern Recognition and Machine Learning 6 ???(1) ?????,?????????????? ????????? ???????? ???????? ????,?????(overlap)?????,?????(Trade-off)?

    7. 2012-6-3 Pattern Recognition and Machine Learning 7 ???(2)

    8. 2012-6-3 Pattern Recognition and Machine Learning 8 Logistic sigmoid ??(1) Logistic sigmoid ??:

    9. 2012-6-3 Pattern Recognition and Machine Learning 9 Logistic sigmoid ??(2) ??????,????????????:

    10. 2012-6-3 Pattern Recognition and Machine Learning 10 Logistic ??(1) ??M??????,???? ????:M ???????????:2M (means) + M(M+1)/2(covariance matrix) + 1(class prior) ???over-fitting ????:?????( regularization ) ?? :??????????(MAP)??

    11. 2012-6-3 Pattern Recognition and Machine Learning 11 Logistic ??(2) ??MLE??Logistic?????

    12. 2012-6-3 Pattern Recognition and Machine Learning 12 Iterative Reweighted LS(1) ??logistic sigmoid ??????,Logistic???????( closed-form solution )? ???????? ????????,??????? ???Newton-Raphson?? Newton-Raphson??:?????????????

    13. 2012-6-3 Pattern Recognition and Machine Learning 13 Iterative Reweighted LS(2) ???????????,?????? ??Logistic????,???IRLS?????

    14. 2012-6-3 Pattern Recognition and Machine Learning 14 ??Logistic?? ???? ? sigmoid?? ???? ? softmax?? ???????????,??????IRLS???????

    15. 2012-6-3 Pattern Recognition and Machine Learning 15 Probit?? Probit??

    16. 2012-6-3 Pattern Recognition and Machine Learning 16 Probit??(1) Probit??

    17. 2012-6-3 Pattern Recognition and Machine Learning 17 Probit??(2) ???logistic??,??probit?????????(activation function)? ????????( outliers )????;??????????????? Logistic??: Probit??: ????????:

    18. 2012-6-3 Pattern Recognition and Machine Learning 18 Laplace??(1) ??Logistic??????????????,????????,???????? Laplace??: ?????????(????) ????????(mode)????Laplace??

    19. 2012-6-3 Pattern Recognition and Machine Learning 19 Laplace??(2) ????: ???(mode)???,??Laplace??; ????:

    20. 2012-6-3 Pattern Recognition and Machine Learning 20 Laplace??(3) ???????: ????,??????(???????) ?????,??????

    21. 2012-6-3 Pattern Recognition and Machine Learning 21 Laplace??(4)

    22. 2012-6-3 Pattern Recognition and Machine Learning 22 ???Logistic??(1) Logistic???,???????sigmoid?????,???? ??Laplace?????? ???? ????:??probit????sigmoid??

    23. 2012-6-3 Pattern Recognition and Machine Learning 23 ???Logistic??(2) ????????????? ??: ????:

    24. 2012-6-3 Pattern Recognition and Machine Learning 24 ???Logistic??(3) ????

    25. 2012-6-3 Pattern Recognition and Machine Learning 25 ???Logistic??(4) ??probit????sigmoid??

    26. 2012-6-3 Pattern Recognition and Machine Learning 26 ?? ????,??? ?? ??????????????????,???? Logistic????IRLS?????; Probit?? Laplace???????? ???Logistic??

    27. 2012-6-3 Pattern Recognition and Machine Learning 27 ??!

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