An Efficient Minibatch Acceptance Test for Metropolis-Hastings

TL;DR

This paper introduces a new minibatch acceptance test for Metropolis-Hastings that significantly reduces computational cost for large datasets, enabling faster sampling with adjustable batch sizes.

Contribution

The authors propose a novel, tunable minibatch acceptance test for Metropolis-Hastings that maintains accuracy while drastically reducing data usage and computational cost.

Findings

Achieves several order-of-magnitude speedups over previous methods

Allows arbitrarily small batch sizes by tuning proposal step size or temperature

Uses a noise-tolerant Barker acceptance test with a new additive correction variable

Abstract

We present a novel Metropolis-Hastings method for large datasets that uses small expected-size minibatches of data. Previous work on reducing the cost of Metropolis-Hastings tests yield variable data consumed per sample, with only constant factor reductions versus using the full dataset for each sample. Here we present a method that can be tuned to provide arbitrarily small batch sizes, by adjusting either proposal step size or temperature. Our test uses the noise-tolerant Barker acceptance test with a novel additive correction variable. The resulting test has similar cost to a normal SGD update. Our experiments demonstrate several order-of-magnitude speedups over previous work.