Asymptotically Optimal Exact Minibatch Metropolis-Hastings

# Asymptotically Optimal Exact Minibatch Metropolis-Hastings

Dec 06, 2020
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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{\methodname{}}, which exposes a tunable trade-off between its batch 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 \methodname{} is asymptotically optimal in terms of the batch size. Empirically, we show \methodname{} outperforms other exact minibatch MH methods on robust linear regression, truncated Gaussian mixtures, and logistic regression. Speakers: Ruqi Zhang, A. Feder Cooper, Christopher De Sa