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Sparse single-index model

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.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-00556652
Contributor : Pierre Alquier <>
Submitted on : Monday, January 17, 2011 - 2:53:13 PM
Last modification on : Friday, June 12, 2020 - 11:02:06 AM
Document(s) archivé(s) le : Monday, April 18, 2011 - 2:35:59 AM

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  • HAL Id : hal-00556652, version 1
  • ARXIV : 1101.3229

Citation

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

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