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info.json
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{
"abstract": "Let <i>(<b>X</b>, Y)</i> be a random pair taking values in <i>ℝ<sup>p</sup> × ℝ</i>. In the so-called single-index model, one has <i>Y=f<sup>*</sup>(θ<sup>* T</sup><b>X</b>)+<b>W</b></i>, where <i>f<sup>*</sup></i> is an unknown univariate measurable function, <i>θ<sup>*</sup></i> is an unknown vector in <i>ℝ<sup>d</sup></i>, and <i>W</i> denotes a random noise satisfying <i> E[<b>W</b>|<b>X</b>]=0</i>. 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 ('<i>p</i> larger than <i>n</i>' 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.",
"authors": [
"Pierre Alquier",
"Gérard Biau"
],
"id": "alquier13a",
"issue": 8,
"pages": [
243,
280
],
"title": "Sparse Single-Index Model",
"volume": 14,
"year": 2013
}