Binary classification based Monte Carlo simulation

TL;DR

This paper introduces a novel approach that uses classifiers to approximate probability density ratios, enabling pdf-free Monte Carlo simulations that are compatible with existing sampling methods.

Contribution

It proposes a new method that replaces traditional pdf ratio computations with classifiers, bridging simulation and classification for improved Monte Carlo algorithms.

Findings

Classifier-based ratio approximation is effective.

The method integrates seamlessly with classical samplers.

It simplifies Monte Carlo simulation without explicit pdfs.

Abstract

Acceptance-rejection (AR), Independent Metropolis Hastings (IMH) or importance sampling (IS) Monte Carlo (MC) simulation algorithms all involve computing ratios of probability density functions (pdfs). On the other hand, classifiers discriminate labeled samples produced by a mixture of two distributions and can be used for approximating the ratio of the two corresponding pdfs.This bridge between simulation and classification enables us to propose pdf-free versions of pdf-ratio-based simulation algorithms, where the ratio is replaced by a surrogate function computed via a classifier. From a probabilistic modeling perspective, our procedure involves a structured energy based model which can easily be trained and is compatible with the classical samplers.