PhD Student, University of British Columbia

Talk Title

Automatic Regenerative Simulation via Non-reversible Simulated Tempering

Abstract

Regenerative simulation is an approach to MCMC that enables massive parallelization of a single Markov chain, while offering computable estimates of the Monte Carlo standard error. Simulated Tempering (ST) is an MCMC algorithm that facilitates simulating
from complex distributions by building a path between the intractable density and an amenable reference distribution. Importantly, ST admits regenerative simulation whenever the reference permits \iid sampling. However, the complexity of tuning ST has hindered its widespread adoption.

In this work we describe and analyze a version of non-reversible simulated tempering (NRST). We show a non-asymptotic domination of NRST over ST, due to the ability of the former to avoid diffusive behavior while traveling along the path of densities. Essential to this result is the development of a metric---which we call Tour Effectiveness (TE)---for evaluating generic simulated tempering algorithms. We show that TE is inversely proportional to a uniform bound on the asymptotic variance of bounded test functions. For this reason, a preliminary estimate of TE can be used to determine in advance the number of tours required to obtain Monte Carlo confidence intervals with prescribed width and coverage for the whole class of bounded functions. Furthermore, by showing how TE relates to the tuning parameters of NRST, we are able to use this metric to guide the development of an automatic tuning procedure. This allows us to seamlessly integrate NRST into existing probabilistic programming languages, thus facilitating its use by practitioners. Finally, we offer extensive experimental evidence of our theoretical claims.

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