Binary Classification Based Monte Carlo Simulation

Acceptance-rejection (AR), Independent Metropolis Hastings (IMH) or Importance Sampling (IS) Monte Carlo (MC) algorithms all involve computing ratios of two probability density functions (pdf) p1 and p0. On the other hand, classifiers discriminate samples produced by a binary mixture and can be used to approximate the ratio of corresponding pdfs. We therefore establish a bridge between simulation and classification, which enables us to propose pdf-free versions of ratio-based simulation algorithms, where the ratio is replaced by a surrogate function computed via a classifier. Our modified samplers are based on very different hypotheses: the knowledge of functions p1 and p0 is relaxed (- they may be totally unknown), and is counterbalanced by the availability of a classification function, which can be obtained from a labelled dataset. From a probabilistic modeling perspective, our procedure involves a structured energy based model which can easily be trained and is structurally compatible with the classical samplers.