Sparse Single-Index Model

作者：Alquier Pierre^*; Biau Gerard

来源：Journal of Machine Learning Research, 2013, 14: 243-280.

• single-index model
• sparsity
• regression estimation
• PAC-Bayesian
• oracle inequality
• reversible jump Markov chain Monte Carlo method

Let (X,Y) be a random pair taking values in R-p x R. In the so-called single-index model, one has Y = f(star)(theta X-star T) + W, where f(star) is an unknown univariate measurable function, theta(star) is an unknown vector in R-d, and W denotes a random noise satisfying E[W vertical bar 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 (%26quot;p larger than n%26quot; 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.

• 出版日期2013-1