PAC-Bayesian risk bounds for group-analysis sparse regression by exponential weighting

Tung Duy Luu, Jalal Fadili and Christophe Chesneau

Journal of Multivariate Analysis, 2019, vol. 171, issue C, 209-233

Abstract: In this paper, we consider a high-dimensional nonparametric regression model with fixed design and iid random errors. We propose an estimator by exponential weighted aggregation with a group-analysis sparsity and a prior on the weights. We prove that our estimator satisfies a sharp group-analysis sparse oracle inequality with a small remainder term that ensures its good theoretical performance. We also propose a forward–backward proximal Langevin Monte Carlo algorithm to sample from the target distribution (which is neither smooth nor log-concave) and derive its convergence guarantees. In turn, this enables us to implement our estimator and validate it with numerical experiments.

Keywords: Exponential weighted aggregation; Forward–backward Langevin Monte Carlo; Frame; Group-analysis sparsity; High-dimensional regression; Sparse learning; Sparse oracle inequality (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.jmva.2018.12.004

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