PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Mixability is Bayes Risk Curvature Relative to Log Loss
Tim van Erven, Mark Reid and Bob Williamson
In: COLT2011, Budapest(2011).

Abstract

Mixability of a loss governs the best possible performance when aggregating expert predictions with respect to that loss. The determination of the mixability constant for binary losses is straightforward but opaque. In the binary case we make this transparent and simpler by characterising mixability in terms of the second derivative of the Bayes risk of proper losses. We then extend this result to multiclass proper losses where there are few existing results. We show that mixability is governed by the Hessian of the Bayes risk, relative to the Hessian of the Bayes risk for log loss. We conclude by comparing our result to other work that bounds prediction performance in terms of the geometry of the Bayes risk.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
ID Code:8980
Deposited By:Bob Williamson
Deposited On:21 February 2012