Group equivariant neural posterior estimation

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.

arXiv comment13+11 pages, 5+8 figures. [v2]: Minor updates to match published version, code available at https://github.com/dingo-gw/dingo

References in corpus (22)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs
• GW170817: Measurements of Neutron Star Radii and Equation of State
• GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run
• Variational Inference with Normalizing Flows
• A gravitational-wave standard siren measurement of the Hubble constant
• Frequency-domain gravitational waves from non-precessing black-hole binaries. II. A phenomenological model for the advanced detector era
• The frontier of simulation-based inference
• Robust parameter estimation for compact binaries with ground-based gravitational-wave observations using the LALInference software library
• Tests of General Relativity with Binary Black Holes from the second LIGO-Virgo Gravitational-Wave Transient Catalog
• A simple model of complete precessing black-hole-binary gravitational waveforms
• Group Equivariant Convolutional Networks
• Bayesian parameter estimation using conditional variational autoencoders for gravitational-wave astronomy
• GWTC-2.1: Deep Extended Catalog of Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run
• Mining gold from implicit models to improve likelihood-free inference
• Fast $\epsilon$-free Inference of Simulation Models with Bayesian Conditional Density Estimation
• Learning Bayesian posteriors with neural networks for gravitational-wave inference
• Sampling using $SU(N)$ gauge equivariant flows
• Automatic Posterior Transformation for Likelihood-Free Inference
• A more effective coordinate system for parameter estimation of precessing compact binaries from gravitational waves
• Lightning-Fast Gravitational Wave Parameter Inference through Neural Amortization