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) $p_{1}$ and $p_{0}$. 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 $p_{1}$ and $p_{0}$ 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.