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hal-00461580, version 3

Mirror averaging with sparsity priors

Arnak Dalalyan () 1, 2, 3, Alexandre Tsybakov () 1, 4

Bernoulli 18, 3 (2012) 914-944

  • 1:  Centre de Recherche en Économie et Statistique (CREST)
  • http://www.crest.fr/
    INSEE – École Nationale de la Statistique et de l'Administration Économique France
  • 2:  IMAGINE
  • http://imagine.enpc.fr/index.html
    CSTB – Ecole des Ponts ParisTech – Université Paris-Est Créteil Val-de-Marne (UPEC) 6 avenue Blaise Pascal - Cité Descartes Champs-sur-Marne 77455 Marne-la-Vallée cedex 2 France
  • 3:  Laboratoire d'Informatique Gaspard-Monge (LIGM)
  • http://igm.univ-mlv.fr/LIGM/
    Université Paris-Est Marne-la-Vallée (UPEMLV) – ESIEE – Ecole des Ponts ParisTech – Fédération de Recherche Bézout – CNRS : UMR8049 Université de Paris-Est - Marne-la-Vallée, Cité Descartes, Bâtiment Copernic, 5 bd Descartes, 77454 Marne-la-Vallée Cedex 2, Inst Gaspard Monge France
  • 4:  Laboratoire de Probabilités et Modèles Aléatoires (LPMA)
  • http://www.proba.jussieu.fr/
    CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot France
  • Available versions :  v1 (2010-03-05) v2 (2010-11-25) v3 (2012-07-27)

    • Bibliographic reference

    • Type of document: Articles in peer-reviewed journal
    • Subject:
      Mathematics/Statistics
      Statistics/Statistics Theory
    • Title: Mirror averaging with sparsity priors
    • Abstract: 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.
    • Fulltext language: English
    • Production date: 2010-03-05
    • DOI: 10.3150/11-BEJ361
    • Journal:
      Bernoulli
      Publisher Bernoulli Society for Mathematical Statistics and Probability
      ISSN 1350-7265 
    • Audience: international
    • Publication date: 2012-10-18
    • Volume: 18
    • Issue: 3
    • Page, identifiant, ...: 914-944
    • Keyword(s): Mirror averaging – progressive mixture – sparsity – aggregation of estimators – oracle inequalities
    • ANR Project:
      Project Id PARCIMONIE

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    • hal-00461580, version 3
    • http://hal.archives-ouvertes.fr/hal-00461580
    • oai:hal.archives-ouvertes.fr:hal-00461580
    • From: Arnak Dalalyan <>
    • Submitted on: Friday, 27 July 2012 00:08:51
    • Updated on: Thursday, 21 March 2013 22:23:09