PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Learning by mirror averaging.
Anatoli Juditsky, Philippe Rigollet and Alexandre Tsybakov
Annals of Statistics 2005.


Given a finite collection of estimators or classifiers, we study the problem of model selection type aggregation, i.e., we construct a new estimator or classifier, called aggregate, which is nearly as good as the best among them with respect to a given risk criterion. We define our aggregate by a simple recursive procedure which solves an auxiliary stochastic linear programming problem related to the original non-linear one and constitutes a special case of the mirror averaging algorithm. We show that the aggregate satisfies sharp oracle inequalities under some general assumptions. The results are applied to several problems including regression, classification and density estimation.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:3863
Deposited By:Alexandre Tsybakov
Deposited On:25 February 2008