Sparse single-index model - Inria - Institut national de recherche en sciences et technologies du numérique
Article Dans Une Revue Journal of Machine Learning Research Année : 2013

Sparse single-index model

Résumé

Let $(\bX, Y)$ be a random pair taking values in $\mathbb R^p \times \mathbb R$. In the so-called single-index model, one has $Y=f^{\star}(\theta^{\star T}\bX)+\bW$, where $f^{\star}$ is an unknown univariate measurable function, $\theta^{\star}$ is an unknown vector in $\mathbb R^d$, and $W$ denotes a random noise satisfying $\mathbb E[\bW|\bX]=0$. 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 simplicity, 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 inequalities 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.
Fichier principal
Vignette du fichier
singleindex6.pdf (387.25 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00556652 , version 1 (17-01-2011)
hal-00556652 , version 2 (05-10-2011)

Identifiants

Citer

Pierre Alquier, Gérard Biau. Sparse single-index model. Journal of Machine Learning Research, 2013, 14, pp.243−280. ⟨hal-00556652v2⟩
562 Consultations
312 Téléchargements

Altmetric

Partager

More