A PAC analysis of a Bayesian estimator
COLT '97 Proceedings of the tenth annual conference on Computational learning theory
COLT' 98 Proceedings of the eleventh annual conference on Computational learning theory
Bayesian Core: A Practical Approach to Computational Bayesian Statistics
Bayesian Core: A Practical Approach to Computational Bayesian Statistics
A New Algorithm for Estimating the Effective Dimension-Reduction Subspace
The Journal of Machine Learning Research
Bayesian estimation and variable selection for single index models
Computational Statistics & Data Analysis
Introduction to Nonparametric Estimation
Introduction to Nonparametric Estimation
Modeling wine preferences by data mining from physicochemical properties
Decision Support Systems
Statistics for High-Dimensional Data: Methods, Theory and Applications
Statistics for High-Dimensional Data: Methods, Theory and Applications
Sparse regression learning by aggregation and Langevin Monte-Carlo
Journal of Computer and System Sciences
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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, θ* is an unknown vector in Rd, and W 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 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.