Open Access
October 2018 On the exponentially weighted aggregate with the Laplace prior
Arnak S. Dalalyan, Edwin Grappin, Quentin Paris
Ann. Statist. 46(5): 2452-2478 (October 2018). DOI: 10.1214/17-AOS1626


In this paper, we study the statistical behaviour of the Exponentially Weighted Aggregate (EWA) in the problem of high-dimensional regression with fixed design. Under the assumption that the underlying regression vector is sparse, it is reasonable to use the Laplace distribution as a prior. The resulting estimator and, specifically, a particular instance of it referred to as the Bayesian lasso, was already used in the statistical literature because of its computational convenience, even though no thorough mathematical analysis of its statistical properties was carried out. The present work fills this gap by establishing sharp oracle inequalities for the EWA with the Laplace prior. These inequalities show that if the temperature parameter is small, the EWA with the Laplace prior satisfies the same type of oracle inequality as the lasso estimator does, as long as the quality of estimation is measured by the prediction loss. Extensions of the proposed methodology to the problem of prediction with low-rank matrices are considered.


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Arnak S. Dalalyan. Edwin Grappin. Quentin Paris. "On the exponentially weighted aggregate with the Laplace prior." Ann. Statist. 46 (5) 2452 - 2478, October 2018.


Received: 1 December 2016; Revised: 1 July 2017; Published: October 2018
First available in Project Euclid: 17 August 2018

zbMATH: 06964338
MathSciNet: MR3845023
Digital Object Identifier: 10.1214/17-AOS1626

Primary: 62J05
Secondary: 62H12

Keywords: Bayesian lasso , Exponential weights , high-dimensional regression , Low-rank matrices , Oracle inequality , Sparsity , Trace regression

Rights: Copyright © 2018 Institute of Mathematical Statistics

Vol.46 • No. 5 • October 2018
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