Sparse single-index model

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Abstract

Let (X,Y) be a random pair taking values in Rp R. In the so-called single-index model, one has Y = f*(θ*TX)+W, where f* is an unknown univariate measurable function, c? is an unknown vector in Rd, andW denotes a random noise satisfying E[W|X] = 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 inecuality, which is more powerful than the best known oracle inecualities for other common procedures of single-index recovery. The proposed method is implemented by means of the reversible jump Markov chain Monte Carlo technicue and its performance is compared with that of standard procedures. © 2013 Pierre Alcuier and Gerard Biau.

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APA

Alcuier, P., & Biau, G. (2013). Sparse single-index model. Journal of Machine Learning Research, 14(1), 243–280.

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