Firefly Monte Carlo: Exact MCMC with Subsets of Data

Dougal Maclaurin Harvard University, Ryan Adams Harvard
Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, PMLR R12:196-205, 2014.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR12-university14e, title = {Firefly {M}onte {C}arlo: Exact {MCMC} with Subsets of Data}, author = {University, Dougal Maclaurin Harvard and Harvard, Ryan Adams}, booktitle = {Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence}, pages = {196--205}, year = {2014}, editor = {Zhang, Nevin L. and Tian, Jin}, volume = {R12}, series = {Proceedings of Machine Learning Research}, month = {23--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r12/main/assets/university14e/university14e.pdf}, url = {https://proceedings.mlr.press/r12/university14e.html}, 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.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Firefly Monte Carlo: Exact MCMC with Subsets of Data %A Dougal Maclaurin Harvard University %A Ryan Adams Harvard %B Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2014 %E Nevin L. Zhang %E Jin Tian %F pmlr-vR12-university14e %I PMLR %P 196--205 %U https://proceedings.mlr.press/r12/university14e.html %V R12 %X 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. %Z Reissued by PMLR on 04 October 2026.
APA
University, D.M.H. & Harvard, R.A.. (2014). Firefly Monte Carlo: Exact MCMC with Subsets of Data. Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R12:196-205 Available from https://proceedings.mlr.press/r12/university14e.html. Reissued by PMLR on 04 October 2026.

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