Asymptotically Optimal Exact Minibatch Metropolis-Hastings

Ruqi Zhang, A. Feder Cooper, Christopher De Sa

Spotlight presentation: Orals & Spotlights Track 25: Probabilistic Models/Statistics
on 2020-12-10T07:50:00-08:00 - 2020-12-10T08:00:00-08:00
Poster Session 6 (more posters)
on 2020-12-10T09:00:00-08:00 - 2020-12-10T11:00:00-08:00
GatherTown: Probabilistic Methods ( Town B0 - Spot D1 )
Join GatherTown
Only iff poster is crowded, join Zoom . Authors have to start the Zoom call from their Profile page / Presentation History.
Abstract: Metropolis-Hastings (MH) is a commonly-used MCMC algorithm, but it can be intractable on large datasets due to requiring computations over the whole dataset. In this paper, we study \emph{minibatch MH} methods, which instead use subsamples to enable scaling. We observe that most existing minibatch MH methods are inexact (i.e. they may change the target distribution), and show that this inexactness can cause arbitrarily large errors in inference. We propose a new exact minibatch MH method, \emph{TunaMH}, which exposes a tunable trade-off between its minibatch size and its theoretically guaranteed convergence rate. We prove a lower bound on the batch size that any minibatch MH method \emph{must} use to retain exactness while guaranteeing fast convergence---the first such bound for minibatch MH---and show TunaMH is asymptotically optimal in terms of the batch size. Empirically, we show TunaMH outperforms other exact minibatch MH methods on robust linear regression, truncated Gaussian mixtures, and logistic regression.

Pre-recorded Spotlight Presentation

Preview Video and Chat

Chat is not available.