PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Safe Learning: bridging the gap between Bayes, MDL and statistical learning theory via empirical convexity
Peter Grünwald
In: COLT 2011, 9-11 July 2011, Budapest, Hungary.

Abstract

We extend Bayesian MAP and Minimum Description Length (MDL) learning by testing whether the data can be substantially more compressed by a mixture of the MDL/MAP distribution with another element of the model, and adjusting the learning rate if this is the case. While standard Bayes and MDL can fail to converge if the model is wrong, the resulting "safe" estimator continues to achieve good rates with wrong models. Moreover, when applied to classication and regression models as considered in statistical learning theory, the approach achieves optimal rates under, e.g., Tsybakov's conditions, and reveals new situations in which we can penalize by -log prior/n rather than the square root thereof.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Theory & Algorithms
ID Code:8846
Deposited By:Peter Grünwald
Deposited On:21 February 2012