Covariance-Controlled Adaptive Langevin Thermostat for Large-Scale Bayesian Sampling

Abstract

Monte Carlo sampling for Bayesian posterior inference is a common approach used in machine learning. The Markov Chain Monte Carlo procedures that are used are often discrete-time analogues of associated stochastic differential equations (SDEs). These SDEs are guaranteed to leave invariant the required posterior distribution. An area of current research addresses the computational benefits of stochastic gradient methods in this setting. Existing techniques rely on estimating the variance or covariance of the subsampling error, and typically assume constant variance. In this article, we propose a covariance-controlled adaptive Langevin thermostat that can effectively dissipate parameter-dependent noise while maintaining a desired target distribution. The proposed method achieves a substantial speedup over popular alternative schemes for large-scale machine learning applications.

References in corpus (3)

• Stochastic Gradient Hamiltonian Monte Carlo
• Bayesian Posterior Sampling via Stochastic Gradient Fisher Scoring
• (Non-) asymptotic properties of Stochastic Gradient Langevin Dynamics

Cited by in corpus (4)

• How Good is the Bayes Posterior in Deep Neural Networks Really?
• Pairwise adaptive thermostats for improved accuracy and stability in dissipative particle dynamics
• Hamiltonian Monte Carlo with Energy Conserving Subsampling
• TATi-Thermodynamic Analytics ToolkIt: TensorFlow-based software for posterior sampling in machine learning applications