Cosmological Parameter Estimation and Inference using Deep Summaries

TL;DR

This paper introduces a novel deep learning-based method for estimating cosmological parameters from high-dimensional data, providing unbiased estimators and accurate posterior distributions even with intractable likelihoods.

Contribution

It proposes a new approach using deep summary statistics and Gaussian process regression for reliable parameter estimation in complex physical models.

Findings

Estimators are unbiased with near-optimal variance.

Posterior estimates closely match true distributions.

Method outperforms comparable approaches.

Abstract

The ability to obtain reliable point estimates of model parameters is of crucial importance in many fields of physics. This is often a difficult task given that the observed data can have a very high number of dimensions. In order to address this problem, we propose a novel approach to construct parameter estimators with a quantifiable bias using an order expansion of highly compressed deep summary statistics of the observed data. These summary statistics are learned automatically using an information maximising loss. Given an observation, we further show how one can use the constructed estimators to obtain approximate Bayes computation (ABC) posterior estimates and their corresponding uncertainties that can be used for parameter inference using Gaussian process regression even if the likelihood is not tractable. We validate our method with an application to the problem of cosmological parameter inference of weak lensing mass maps. We show in that case that the constructed estimators are unbiased and have an almost optimal variance, while the posterior distribution obtained with the Gaussian process regression is close to the true posterior and performs better or equally well than comparable methods.