Automatic physical inference with information maximising neural networks

TL;DR

This paper introduces a neural network-based method called IMNNs that automatically finds optimal data summaries maximizing Fisher information, enabling accurate likelihood-free inference for complex scientific data.

Contribution

The paper presents a novel simulation-based neural network technique that automatically derives non-linear data summaries maximizing Fisher information, improving inference accuracy in complex scenarios.

Findings

IMNN summaries produce nearly exact posteriors in test cases.

IMNNs outperform linear compression in complex astrophysical data.

IMNNs are robust in extracting optimal summaries even with non-linear data.

Abstract

Compressing large data sets to a manageable number of summaries that are informative about the underlying parameters vastly simplifies both frequentist and Bayesian inference. When only simulations are available, these summaries are typically chosen heuristically, so they may inadvertently miss important information. We introduce a simulation-based machine learning technique that trains artificial neural networks to find non-linear functionals of data that maximise Fisher information: information maximising neural networks (IMNNs). In test cases where the posterior can be derived exactly, likelihood-free inference based on automatically derived IMNN summaries produces nearly exact posteriors, showing that these summaries are good approximations to sufficient statistics. In a series of numerical examples of increasing complexity and astrophysical relevance we show that IMNNs are robustly capable of automatically finding optimal, non-linear summaries of the data even in cases where linear compression fails: inferring the variance of Gaussian signal in the presence of noise; inferring cosmological parameters from mock simulations of the Lyman-{\alpha} forest in quasar spectra; and inferring frequency-domain parameters from LISA-like detections of gravitational waveforms. In this final case, the IMNN summary outperforms linear data compression by avoiding the introduction of spurious likelihood maxima. We anticipate that the automatic physical inference method described in this paper will be essential to obtain both accurate and precise cosmological parameter estimates from complex and large astronomical data sets, including those from LSST and Euclid.