Statistical applications of contrastive learning

TL;DR

This paper explores how contrastive learning can serve as a practical alternative to likelihood-based methods in statistical inference, especially for complex models where likelihoods are intractable.

Contribution

It introduces contrastive learning techniques and demonstrates their application to parameter estimation, Bayesian inference, and experimental design in challenging statistical models.

Findings

Contrastive learning provides a feasible alternative to likelihood-based inference.

The methods improve computational efficiency for energy-based and simulator-based models.

Applications include enhanced parameter estimation and experimental design strategies.

Abstract

The likelihood function plays a crucial role in statistical inference and experimental design. However, it is computationally intractable for several important classes of statistical models, including energy-based models and simulator-based models. Contrastive learning is an intuitive and computationally feasible alternative to likelihood-based learning. We here first provide an introduction to contrastive learning and then show how we can use it to derive methods for diverse statistical problems, namely parameter estimation for energy-based models, Bayesian inference for simulator-based models, as well as experimental design.