Firefly Monte Carlo: Exact MCMC with Subsets of Data

TL;DR

Firefly Monte Carlo (FlyMC) is an exact MCMC algorithm that efficiently samples from the posterior using only a subset of data likelihoods, enabling scalable Bayesian inference on large datasets.

Contribution

FlyMC introduces an auxiliary variable MCMC method that maintains exactness while significantly reducing likelihood evaluations, compatible with various MCMC algorithms.

Findings

FlyMC is over ten times faster than standard MCMC on large datasets.

It produces exact posterior samples, unlike approximate methods.

The method scales efficiently with data size.

Abstract

Markov chain Monte Carlo (MCMC) is a popular and successful general-purpose tool for Bayesian inference. However, MCMC cannot be practically applied to large data sets because of the prohibitive cost of evaluating every likelihood term at every iteration. Here we present Firefly Monte Carlo (FlyMC) an auxiliary variable MCMC algorithm that only queries the likelihoods of a potentially small subset of the data at each iteration yet simulates from the exact posterior distribution, in contrast to recent proposals that are approximate even in the asymptotic limit. FlyMC is compatible with a wide variety of modern MCMC algorithms, and only requires a lower bound on the per-datum likelihood factors. In experiments, we find that FlyMC generates samples from the posterior more than an order of magnitude faster than regular MCMC, opening up MCMC methods to larger datasets than were previously considered feasible.