On Contrastive Learning for Likelihood-free Inference
This work provides a theoretical unification for researchers in likelihood-free inference, but it is incremental as it builds on established methods without introducing new paradigms.
The paper tackles the problem of likelihood-free inference in stochastic simulator models by unifying two existing approaches under a general contrastive learning scheme, clarifying their implementation and comparison.
Likelihood-free methods perform parameter inference in stochastic simulator models where evaluating the likelihood is intractable but sampling synthetic data is possible. One class of methods for this likelihood-free problem uses a classifier to distinguish between pairs of parameter-observation samples generated using the simulator and pairs sampled from some reference distribution, which implicitly learns a density ratio proportional to the likelihood. Another popular class of methods fits a conditional distribution to the parameter posterior directly, and a particular recent variant allows for the use of flexible neural density estimators for this task. In this work, we show that both of these approaches can be unified under a general contrastive learning scheme, and clarify how they should be run and compared.