Sparse single-index model

Pierre Alquier; Gérard Biau

hal-00556652, version 1

Sparse single-index model

Pierre Alquier () ^1, 2, Gérard Biau () ^1, 3, 4

(2011-01-17)

Abstract: 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.

1: Laboratoire de Probabilités et Modèles Aléatoires (LPMA)
CNRS : UMR7599 – Université Pierre et Marie Curie (UPMC) - Paris VI – Université Paris VII - Paris Diderot
2: Centre de Recherche en Économie et Statistique (CREST)
INSEE – École Nationale de la Statistique et de l'Administration Économique
3: Laboratoire de Statistique Théorique et Appliquée (LSTA)
Université Pierre et Marie Curie (UPMC) - Paris VI
4: Département de Mathématiques et Applications (DMA)
CNRS : UMR8553 – Ecole normale supérieure de Paris - ENS Paris

hal-00556652, version 1
http://hal.archives-ouvertes.fr/hal-00556652
oai:hal.archives-ouvertes.fr:hal-00556652
From: Pierre Alquier <>
Submitted on: Monday, 17 January 2011 14:53:13
Updated on: Monday, 17 January 2011 15:37:02

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arXiv: 1101.3229

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