AMAGOLD: Amortized Metropolis Adjustment for Efficient Stochastic Gradient MCMC
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Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:21422152, 2020.
Abstract
Stochastic gradient Hamiltonian Monte Carlo (SGHMC) is an efficient method for sampling from continuous distributions. It is a faster alternative to HMC: instead of using the whole dataset at each iteration, SGHMC uses only a subsample. This improves performance, but introduces bias that can cause SGHMC to converge to the wrong distribution. One can prevent this using a step size that decays to zero, but such a step size schedule can drastically slow down convergence. To address this tension, we propose a novel secondorder SGMCMC algorithm—AMAGOLD—that infrequently uses MetropolisHastings (MH) corrections to remove bias. The infrequency of corrections amortizes their cost. We prove AMAGOLD converges to the target distribution with a fixed, rather than a diminishing, step size, and that its convergence rate is at most a constant factor slower than a fullbatch baseline. We empirically demonstrate AMAGOLD’s effectiveness on synthetic distributions, Bayesian logistic regression, and Bayesian neural networks.
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