Simulation-based Inference with the Generalized Kullback-Leibler Divergence
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.
Cite
@article{arxiv.2310.01808,
title = {Simulation-based Inference with the Generalized Kullback-Leibler Divergence},
author = {Benjamin Kurt Miller and Marco Federici and Christoph Weniger and Patrick Forré},
journal= {arXiv preprint arXiv:2310.01808},
year = {2023}
}
Comments
Accepted at Synergy of Scientific and Machine Learning Modeling ICML 2023 Workshop https://syns-ml.github.io/2023/contributions/