Simulation-based Inference with the Generalized Kullback-Leibler Divergence
This work addresses a methodological bottleneck in Simulation-based Inference for researchers, offering a hybrid approach that combines normalized and unnormalized models, though it appears incremental in nature.
The paper tackles the challenge of fitting unnormalized surrogate models in Simulation-based Inference by proposing a generalized Kullback-Leibler divergence that accounts for normalization constants, unifying Neural Posterior Estimation and Neural Ratio Estimation into a single objective and presenting benchmark results.
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.