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Suboptimality of MDL and Bayes in Classification under Misspecification
Published on Feb 25, 20073209 Views
We show that forms of Bayesian and MDL learning that are often applied to classification problems can be *statistically inconsistent*. We present a large family of classifiers and a distribution such
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Suboptimality of Bayes and MDL in Classification00:02
Our Result00:29
Why is this interesting?01:17
Menu02:39
Classification03:22
Classification Models04:26
Generalization Error05:05
Learning Algorithms06:02
Consistent Learning Algorithms06:38
Consistent Learning Algorithms07:57
Main Result08:09
Main Result12:54
Remainder of Talk13:07
Bayesian Learning of Classifiers13:40
classifiers probability distrs.14:53
Logistic transformation - intuition16:25
Logistic transformation - intuition17:26
Logistic transformation - intuition18:42
classifiers probability distrs.18:48
Logistic transformation - intuition19:25
Logistic transformation - intuition21:02
Main Result24:30
Definition of . 24:55
Issues/Remainder of Talk27:21
Scenario27:36
Scenario – II: Definition of true D29:35
Result: 31:16
Theorem 137:20
Scenario – II: Definition of true D37:57
Theorem 1, extended 39:33
How ‘natural’ is scenario?42:46
Scenario – II: Definition of true D43:00
Thm 2: full Bayes result is ‘tight’ 45:46
Theorem 247:38
Thm 2: full Bayes result is ‘tight’ 49:18
Proof Sketch49:46
Proof Sketch51:29
Proof Sketch53:45
Proof Sketch54:23
Wait a minute…55:35
Bayes predicts too well58:52
Bayesian Consistency Results01:00:11
Bayesian Consistency Results01:00:47
Bayesian consistency under misspecification01:02:58
Bayesian consistency under misspecification01:03:56
Conclusion01:05:21