Efficient stochastic optimisation by unadjusted Langevin Monte Carlo. Application to maximum marginal likelihood and empirical Bayesian estimation - Archive ouverte HAL Access content directly
Journal Articles Statistics and Computing Year : 2020

Efficient stochastic optimisation by unadjusted Langevin Monte Carlo. Application to maximum marginal likelihood and empirical Bayesian estimation

Abstract

Stochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric empirical Bayesian estimation. Combined with Markov chain Monte Carlo algorithms, these stochastic optimisation methods have been successfully applied to a wide range of problems in science and industry. However, this strategy scales poorly to large problems because of methodological and theoretical difficulties related to using high-dimensional Markov chain Monte Carlo algorithms within a stochastic approximation scheme. This paper proposes to address these difficulties by using unadjusted Langevin algorithms to construct the stochastic approximation. This leads to a highly efficient stochastic optimisation methodology with favourable convergence properties that can be quantified explicitly and easily checked. The proposed methodology is demonstrated with three experiments, including a challenging application to high-dimensional statistical audio analysis and a sparse Bayesian logistic regression with random effects problem.
Fichier principal
Vignette du fichier
main (3).pdf (1.24 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01978999 , version 1 (12-01-2019)
hal-01978999 , version 2 (02-12-2020)

Identifiers

Cite

Valentin de Bortoli, Alain Durmus, Marcelo Pereyra, Ana Fernandez Vidal. Efficient stochastic optimisation by unadjusted Langevin Monte Carlo. Application to maximum marginal likelihood and empirical Bayesian estimation. Statistics and Computing, 2020, ⟨10.1007/s11222-020-09986-y⟩. ⟨hal-01978999v2⟩
166 View
195 Download

Altmetric

Share

Gmail Facebook X LinkedIn More