26453 articles – 20338 Notices  [english version]
 Fiche détaillée Preprint, Working Paper, Document sans référence, etc.
 Versions disponibles : v1 (17-01-2011) v2 (06-10-2011)
Liste des fichiers attachés à ce document :
 PDF
 singleindex5.pdf(387.3 KB)
 PS
 singleindex5.ps(913.1 KB)
 Sparse single-index model
 Pierre Alquier1, 2, Gérard Biau1, 3, 4
 The single-index model is known to offer a flexible way to model a variety of high-dimensional real-world phenomena. However, despite its relative implicity, this dimension reduction scheme is faced with severe complications as soon as the underlying dimension becomes larger than the number of observations (p larger than n'' paradigm). To circumvent this difficulty, we consider the single-index model estimation problem from a sparsity perspective using a PAC-Bayesian approach. On the theoretical side, we offer a sharp oracle inequality, which is more powerful than the best known oracle inequality for other common procedures of single-index recovery. The proposed method is implemented by means of the reversible jump Markov chain Monte Carlo technique and its performance is compared with that of standard procedures.
 Mots Clés : Nonparametric statistics – single-index model – sparsity – PAC-Bayesian inequalities – oracle inequalities – MCMC.
 hal-00556652, version 1 http://hal.archives-ouvertes.fr/hal-00556652 oai:hal.archives-ouvertes.fr:hal-00556652 Contributeur : Pierre Alquier <> Soumis le : Lundi 17 Janvier 2011, 14:53:13 Dernière modification le : Lundi 17 Janvier 2011, 15:37:02