26751 articles – 20452 references  [version française]
Detailed view Article in peer-reviewed journal
Bernoulli 18, 3 (2012) 914-944
Available versions:
Attached file list to this document: 
PDF
Bernoulli-revised5.pdf(314.7 KB)
PS
Bernoulli-revised5.ps(982.2 KB)
Mirror averaging with sparsity priors
Arnak Dalalyan1, Alexandre Tsybakov1, 2

We consider the problem of aggregating the elements of a (possibly infinite) dictionary for building a decision procedure, that aims at minimizing a given criterion. Along with the dictionary, an independent identically distributed training sample is available, on which the performance of a given procedure can be tested. In a fairly general set-up, we establish an oracle inequality for the Mirror Averaging aggregate based on any prior distribution. This oracle inequality is applied in the context of sparse coding for different problems of statistics and machine learning such as regression, density estimation and binary classification.
1:  CREST - Centre de Recherche en Économie et Statistique
2:  LPMA - Laboratoire de Probabilités et Modèles Aléatoires
Mirror averaging – progressive mixture – sparsity – aggregation of estimators – oracle inequalities