Robust Optimisation Monte Carlo

Abstract: This paper is on Bayesian inference for parametric statistical models that are defined by a stochastic simulator which specifies how data is generated. Exact sampling is then possible but evaluating the likelihood function is typically prohibitively expensive. Approximate Bayesian Computation (ABC) is a framework to perform approximate inference in such situations. While basic ABC algorithms are widely applicable, they are notoriously slow and much research has focused on increasing their efficiency. Optimisation Monte Carlo (OMC) has recently been proposed as an efficient and embarrassingly parallel method that leverages optimisation to accelerate the inference. In this paper, we demonstrate an important previously unrecognised failure mode of OMC: It generates strongly overconfident approximations by collapsing regions of similar or near-constant likelihood into a single point. We propose an efficient, robust generalisation of OMC that corrects this. It makes fewer assumptions, retains the main benefits of OMC, and can be performed either as post-processing to OMC or as a stand-alone computation. We demonstrate the effectiveness of the proposed Robust OMC on toy examples and tasks in inverse-graphics where we perform Bayesian inference with a complex image renderer.