Subsampling Error in Stochastic Gradient Langevin Diffusions

arXiv:2305.13882v2 Announce Type: replace-cross
Abstract: The Stochastic Gradient Langevin Dynamics (SGLD) are popularly used to approximate Bayesian posterior distributions in statistical learning procedures with large-scale data. As opposed to many usual Markov chain Monte Carlo (MCMC) algorithms, SGLD is not stationary with respect to the posterior distribution; two sources of error appear: The first error is introduced by an Euler--Maruyama discretisation of a Langevin diffusion process, the second error comes from the data subsampling that enables its use in large-scale …

abstract algorithms arxiv bayesian cs.lg data distribution dynamics error gradient markov mcmc posterior scale stat.co statistical stat.ml stochastic type