Sparse single-index model

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

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 CREST - Centre de Recherche en Économie et Statistique
3 LSTA - Laboratoire de Statistique Théorique et Appliquée
4 DMA - Département de Mathématiques et Applications - ENS Paris

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.; MCMC

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Pierre Alquier, Gérard Biau. Sparse single-index model. 2011. ⟨hal-00556652v1⟩