A Shrinkage-Thresholding Metropolis Adjusted Langevin Algorithm for Bayesian Variable Selection

Amandine Schreck; Gersende Fort; Sylvain Le Corff; Eric Moulines

doi:10.1109/JSTSP.2015.2496546

A Shrinkage-Thresholding Metropolis Adjusted Langevin Algorithm for Bayesian Variable Selection

Amandine Schreck
, Gersende Fort
, Sylvain Le Corff
, Eric Moulines

Research output: Contribution to journal › Article › peer-review

Abstract

This paper introduces a new Markov Chain Monte Carlo method for Bayesian variable selection in high dimensional settings. The algorithm is a Hastings-Metropolis sampler with a proposal mechanism which combines a Metropolis Adjusted Langevin (MALA) step to propose local moves associated with a shrinkage-thresholding step allowing to propose new models. The geometric ergodicity of this new trans-dimensional Markov Chain Monte Carlo sampler is established. An extensive numerical experiment, on simulated and real data, is presented to illustrate the performance of the proposed algorithm in comparison with some more classical trans-dimensional algorithms.

Original language	English
Article number	7312917
Pages (from-to)	366-375
Number of pages	10
Journal	IEEE Journal on Selected Topics in Signal Processing
Volume	10
Issue number	2
DOIs	https://doi.org/10.1109/JSTSP.2015.2496546
Publication status	Published - 1 Mar 2016
Externally published	Yes

Keywords

Bayesian variable selection
Markov chain Monte Carlo (MCMC)
Metropolis Adjusted Langevin Algorithm (MALA)
proximal operators
sparsity

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10.1109/JSTSP.2015.2496546

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title = "A Shrinkage-Thresholding Metropolis Adjusted Langevin Algorithm for Bayesian Variable Selection",

abstract = "This paper introduces a new Markov Chain Monte Carlo method for Bayesian variable selection in high dimensional settings. The algorithm is a Hastings-Metropolis sampler with a proposal mechanism which combines a Metropolis Adjusted Langevin (MALA) step to propose local moves associated with a shrinkage-thresholding step allowing to propose new models. The geometric ergodicity of this new trans-dimensional Markov Chain Monte Carlo sampler is established. An extensive numerical experiment, on simulated and real data, is presented to illustrate the performance of the proposed algorithm in comparison with some more classical trans-dimensional algorithms.",

keywords = "Bayesian variable selection, Markov chain Monte Carlo (MCMC), Metropolis Adjusted Langevin Algorithm (MALA), proximal operators, sparsity",

author = "Amandine Schreck and Gersende Fort and \{Le Corff\}, Sylvain and Eric Moulines",

note = "Publisher Copyright: {\textcopyright} 2015 IEEE.",

year = "2016",

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doi = "10.1109/JSTSP.2015.2496546",

language = "English",

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AU - Schreck, Amandine

AU - Fort, Gersende

AU - Le Corff, Sylvain

AU - Moulines, Eric

PY - 2016/3/1

Y1 - 2016/3/1

N2 - This paper introduces a new Markov Chain Monte Carlo method for Bayesian variable selection in high dimensional settings. The algorithm is a Hastings-Metropolis sampler with a proposal mechanism which combines a Metropolis Adjusted Langevin (MALA) step to propose local moves associated with a shrinkage-thresholding step allowing to propose new models. The geometric ergodicity of this new trans-dimensional Markov Chain Monte Carlo sampler is established. An extensive numerical experiment, on simulated and real data, is presented to illustrate the performance of the proposed algorithm in comparison with some more classical trans-dimensional algorithms.

AB - This paper introduces a new Markov Chain Monte Carlo method for Bayesian variable selection in high dimensional settings. The algorithm is a Hastings-Metropolis sampler with a proposal mechanism which combines a Metropolis Adjusted Langevin (MALA) step to propose local moves associated with a shrinkage-thresholding step allowing to propose new models. The geometric ergodicity of this new trans-dimensional Markov Chain Monte Carlo sampler is established. An extensive numerical experiment, on simulated and real data, is presented to illustrate the performance of the proposed algorithm in comparison with some more classical trans-dimensional algorithms.

KW - Bayesian variable selection

KW - Markov chain Monte Carlo (MCMC)

KW - Metropolis Adjusted Langevin Algorithm (MALA)

KW - proximal operators

KW - sparsity

UR - https://www.scopus.com/pages/publications/84962861058

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DO - 10.1109/JSTSP.2015.2496546

M3 - Article

AN - SCOPUS:84962861058

SN - 1932-4553

VL - 10

SP - 366

EP - 375

JO - IEEE Journal on Selected Topics in Signal Processing

JF - IEEE Journal on Selected Topics in Signal Processing

IS - 2

M1 - 7312917

ER -

A Shrinkage-Thresholding Metropolis Adjusted Langevin Algorithm for Bayesian Variable Selection

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Keywords

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