Statistical applications of contrastive learning

It is a computationally feasible yet statistically principled alternative to likelihood-based learning when the likelihood function is too expensive to compute and thus has wide applicability. In this paper we focus on the statistical side of contrastive learning rather than on a particular application domain. We first explain the principles of contrastive learning and then show how we can use it to solve a diverse set of difficult statistical tasks, namely (1) parameter estimation for energy-based models, (2) Bayesian inference for simulator-based models, as well as (3) experimental design. We will introduce these problems in detail and explain when and why likelihood-based learning becomes computationally infeasible. The three problems involve different models as well as tasks--inference versus experimental design.