Neural Posterior Regularization for Likelihood-Free Inference

TL;DR

This paper introduces Neural Posterior Regularization (NPR), a technique to improve likelihood-free Bayesian inference, especially for complex, multi-modal posteriors in high-dimensional simulation outputs, enhancing efficiency and accuracy.

Contribution

The paper proposes a novel regularization method, NPR, with a closed-form solution, to better explore the input space in likelihood-free inference tasks.

Findings

NPR significantly improves benchmark performance across diverse simulation tasks.

The closed-form solution facilitates analysis of the regularization effect.

NPR effectively handles multi-modal, high-dimensional posteriors.

Abstract

A simulation is useful when the phenomenon of interest is either expensive to regenerate or irreproducible with the same context. Recently, Bayesian inference on the distribution of the simulation input parameter has been implemented sequentially to minimize the required simulation budget for the task of simulation validation to the real-world. However, the Bayesian inference is still challenging when the ground-truth posterior is multi-modal with a high-dimensional simulation output. This paper introduces a regularization technique, namely Neural Posterior Regularization (NPR), which enforces the model to explore the input parameter space effectively. Afterward, we provide the closed-form solution of the regularized optimization that enables analyzing the effect of the regularization. We empirically validate that NPR attains the statistically significant gain on benchmark performances for diverse simulation tasks.