Sparse single-index model

Abstract : 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.
Type de document :
Article dans une revue
Journal of Machine Learning Research, Journal of Machine Learning Research, 2013, 14, pp.243−280
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Contributeur : Pierre Alquier <>
Soumis le : mercredi 5 octobre 2011 - 11:47:17
Dernière modification le : jeudi 9 février 2017 - 15:42:16
Document(s) archivé(s) le : mardi 13 novembre 2012 - 15:12:00


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  • HAL Id : hal-00556652, version 2
  • ARXIV : 1101.3229



Pierre Alquier, Gérard Biau. Sparse single-index model. Journal of Machine Learning Research, Journal of Machine Learning Research, 2013, 14, pp.243−280. <hal-00556652v2>



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