Efficient Bayesian Inference for Nested Simulators

Bradley Gram-Hansen, Christian Schroeder de Witt, Robert Zinkov, Saeid Naderiparizi, Adam Scibior, Andreas Munk, Frank Wood, Mehrdad Ghadiri, Philip Torr, Yee Whye Teh, Atilim Gunes Baydin, Tom Rainforth

Keywords: generative modelling, Bayesian Inference, Simulators, Probabilistic programming, nested Monte Carlo, MCMC methods

Abstract: We introduce two approaches for conducting efficient Bayesian inference in stochastic simulators containing nested stochastic sub-procedures, i.e., internal procedures for which the density cannot be calculated directly such as rejection sampling loops. The resulting class of simulators are used extensively throughout the sciences and can be interpreted as probabilistic generative models. However, drawing inferences from them poses a substantial challenge due to the inability to evaluate even their unnormalised density, preventing the use of many standard inference procedures like Markov Chain Monte Carlo (MCMC). To address this, we introduce inference algorithms based on a two-step approach that first approximates the conditional densities of the individual sub-procedures, before using these approximations to run MCMC methods on the full program. Because the sub-procedures can be dealt with separately and are lower-dimensional than that of the overall problem, this two-step process allows them to be isolated and thus be tractably dealt with, without placing restrictions on the overall dimensionality of the problem. We demonstrate the utility of our approach on a simple, artificially constructed simulator.

TL;DR: We introduce two approaches for efficient and scalable inference in stochastic simulators for which the density cannot be evaluated directly due to, for example, rejection sampling loops.