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Efficient stochastic optimisation by unadjusted Langevin Monte Carlo

机译：未经调整的Langevin Monte Carlo有效的随机优化

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摘要

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 statistical audio analysis and a sparse Bayesian logistic regression with random effects problem.
机译：随机近似方法在涉及棘手似然函数的最大似然估计问题中起到核心作用，例如缺失或不完整的问题中出现的边际似然，以及参数经验贝叶斯估计。结合马尔可夫链蒙特卡罗算法，这些随机优化方法已成功应用于各种科学和工业问题。然而，由于与在随机近似方案中使用高维马尔可夫链蒙特卡罗算法相关的方法论和理论困难，这种策略缩放了巨大问题。本文提出通过使用未调整的Langevin算法来解决这些困难来构建随机近似。这导致高效的随机优化方法，其具有良好的收敛性，可以明确且容易地检查。拟议的方法是用三个实验证明，包括统计音频分析的具有挑战性的应用以及随机效应问题的稀疏贝叶斯逻辑回归。

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