# Automatic physical inference

**Authors:** Tom Charnock, Guilhem Lavaux, Benjamin D. Wandelt  
**arXiv:** [1802.03537](https://arxiv.org/abs/1802.03537)  
**Date:** 2018-02-10  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1802.03537v1/

## Key points

- Information Maximizing Neural Networks (IMNNs) are proposed as a technique for compressing large data sets into informative summaries in statistical inference.
- IMNNs use simulation-based reinforcement learning to train artificial neural networks to identify non-linear functionals of data that maximize Fisher information.
- IMNNs produce nearly exact posteriors when applied to test cases with exact posterior distributions, indicating that the summaries serve as good approximations to sufficient statistics.
- IMNNs are robust and outperform linear compression methods in various numerical examples, including accurately inferring the variance of Gaussian signals in the presence of noise, estimating cosmological parameters from mock simulations of the Lyman-$\alpha$ forest, and determining frequency-domain parameters from gravitational waveforms.
- The authors anticipate that IMNNs will be essential for obtaining accurate estimates for cosmological parameters from complex astronomical data sets.
- Potential applications of this research include upcoming projects such as LSST, Euclid, and WFIRST.

## Summary

In the field of statistical inference, compressing large data sets into a smaller number of informative summaries is crucial for both frequentist and Bayesian approaches. To address this issue, the authors propose a novel technique called Information Maximizing Neural Networks (IMNNs), which employ simulation-based reinforcement learning to train artificial neural networks to identify non-linear functionals of data that maximize Fisher information. The authors demonstrate the effectiveness of IMNNs by applying them to various test cases where the posterior distribution can be derived exactly. In these cases, likelihood-free inference based on automatically derived IMNN summaries produces nearly exact posteriors, indicating that these summaries serve as good approximations to sufficient statistics. The authors also present a series of numerical examples with increasing complexity and astrophysical relevance to showcase the robustness of IMNNs in finding optimal non-linear summaries even in situations where linear compression methods fail. Specifically, they show that IMNNs can accurately infer the variance of Gaussian signals in the presence of noise, estimate cosmological parameters from mock simulations of the Lyman-$\alpha$ forest in quasar spectra, and determine frequency-domain parameters from LISA-like detections of gravitational waveforms. Notably, in the case of inferring frequency-domain parameters from gravitational waveforms, IMNN summaries outperform linear data compression techniques by avoiding spurious likelihood maxima. The authors anticipate that their automatic physical inference method will play an essential role in obtaining accurate and precise estimates for cosmological parameters from complex and large astronomical data sets. They highlight its potential applications in upcoming projects such as LSST (Large Synoptic Survey Telescope), Euclid, and WFIRST (Wide Field Infrared Survey Telescope). Overall, this research introduces a promising approach for improving statistical inference by automating the identification of informative data summaries using neural networks trained through simulation-based reinforcement learning.