Group equivariant neural posterior estimation

TL;DR

The paper introduces GNPE, a novel method that incorporates geometric equivariances into neural posterior estimation, significantly improving inference accuracy and speed in scientific inverse problems.

Contribution

GNPE provides a flexible, architecture-independent approach to embed equivariances into neural density estimators for simulation-based inference.

Findings

Achieves state-of-the-art accuracy in astrophysical inference

Reduces inference times by three orders of magnitude

Effectively incorporates equivariances into neural networks

Abstract

Simulation-based inference with conditional neural density estimators is a powerful approach to solving inverse problems in science. However, these methods typically treat the underlying forward model as a black box, with no way to exploit geometric properties such as equivariances. Equivariances are common in scientific models, however integrating them directly into expressive inference networks (such as normalizing flows) is not straightforward. We here describe an alternative method to incorporate equivariances under joint transformations of parameters and data. Our method -- called group equivariant neural posterior estimation (GNPE) -- is based on self-consistently standardizing the "pose" of the data while estimating the posterior over parameters. It is architecture-independent, and applies both to exact and approximate equivariances. As a real-world application, we use GNPE for amortized inference of astrophysical binary black hole systems from gravitational-wave observations. We show that GNPE achieves state-of-the-art accuracy while reducing inference times by three orders of magnitude.