Simulation-based Inference with the Generalized Kullback-Leibler Divergence

TL;DR

This paper introduces a generalized Kullback-Leibler divergence for simulation-based inference, enabling effective fitting of unnormalized models and unifying neural posterior and ratio estimation methods.

Contribution

It proposes a novel divergence measure that handles unnormalized distributions, unifies existing neural inference methods, and explores hybrid models with improved performance.

Findings

Unified framework for neural posterior and ratio estimation

Effective fitting of unnormalized models in simulation-based inference

Benchmark results demonstrating method efficacy

Abstract

In Simulation-based Inference, the goal is to solve the inverse problem when the likelihood is only known implicitly. Neural Posterior Estimation commonly fits a normalized density estimator as a surrogate model for the posterior. This formulation cannot easily fit unnormalized surrogates because it optimizes the Kullback-Leibler divergence. We propose to optimize a generalized Kullback-Leibler divergence that accounts for the normalization constant in unnormalized distributions. The objective recovers Neural Posterior Estimation when the model class is normalized and unifies it with Neural Ratio Estimation, combining both into a single objective. We investigate a hybrid model that offers the best of both worlds by learning a normalized base distribution and a learned ratio. We also present benchmark results.