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. Index Terms—Bayesian variable selection, Metropolis Adjusted Langevin Algorithm (MALA), Markov chain Monte Carlo (MCMC), proximal operators, sparsity.
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Submitted on : Monday, December 19, 2016 - 8:11:08 PM
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Amandine Schreck, Gersende Fort, Sylvain Le Corff, Éric Moulines. A Shrinkage-Thresholding Metropolis Adjusted Langevin Algorithm for Bayesian Variable Selection. IEEE Journal of Selected Topics in Signal Processing, IEEE, 2016, 10, pp.366 - 375. ⟨10.1109/JSTSP.2015.2496546⟩. ⟨hal-01418960⟩

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