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

作者：Schreck Amandine^*; Fort Gersende^*; Le Corff Sylvain^*; Moulines Eric^*

来源：IEEE Journal of Selected Topics in Signal Processing, 2016, 10(2): 366-375.

DOI：10.1109/JSTSP.2015.2496546

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

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.

• 出版日期2016-3
• 单位TELECOM ParisTech