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• W2123222757 abstract "In regular statistical models, the leave-one-out cross-validation is asymptotically equivalent to the Akaike information criterion. However, since many learning machines are singular statistical models, the asymptotic behavior of the cross-validation remains unknown. In previous studies, we established the singular learning theory and proposed a widely applicable information criterion, the expectation value of which is asymptotically equal to the average Bayes generalization loss. In the present paper, we theoretically compare the Bayes cross-validation loss and the widely applicable information criterion and prove two theorems. First, the Bayes cross-validation loss is asymptotically equivalent to the widely applicable information criterion as a random variable. Therefore, model selection and hyperparameter optimization using these two values are asymptotically equivalent. Second, the sum of the Bayes generalization error and the Bayes cross-validation error is asymptotically equal to 2λ/n, where λ is the real log canonical threshold and n is the number of training samples. Therefore the relation between the cross-validation error and the generalization error is determined by the algebraic geometrical structure of a learning machine. We also clarify that the deviance information criteria are different from the Bayes cross-validation and the widely applicable information criterion." @default.
• W2123222757 created "2016-06-24" @default.
• W2123222757 creator A5089768991 @default.
• W2123222757 date "2010-03-01" @default.
• W2123222757 modified "2023-10-06" @default.
• W2123222757 title "Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory" @default.
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