Lossless, Scalable Implicit Likelihood Inference for Cosmological Fields

TL;DR

This paper demonstrates that simulation-based inference with neural network compressed summaries can nearly match the exact Bayesian posteriors in cosmological field analysis, offering a computationally efficient alternative to traditional likelihood methods.

Contribution

It introduces a neural network-based summary statistic approach that retains all information and enables nearly lossless, scalable inference in cosmological data analysis, bypassing complex likelihood evaluations.

Findings

Neural network summaries do not lose information compared to full field analysis.

Simulation-based inference with these summaries nearly recovers exact posteriors.

Implicit inference is computationally cheaper than explicit likelihood methods.

Abstract

We present a comparison of simulation-based inference to full, field-based analytical inference in cosmological data analysis. To do so, we explore parameter inference for two cases where the information content is calculable analytically: Gaussian random fields whose covariance depends on parameters through the power spectrum; and correlated lognormal fields with cosmological power spectra. We compare two inference techniques: i) explicit field-level inference using the known likelihood and ii) implicit likelihood inference with maximally informative summary statistics compressed via Information Maximising Neural Networks (IMNNs). We find that a) summaries obtained from convolutional neural network compression do not lose information and therefore saturate the known field information content, both for the Gaussian covariance and the lognormal cases, b) simulation-based inference using these maximally informative nonlinear summaries recovers nearly losslessly the exact posteriors of field-level inference, bypassing the need to evaluate expensive likelihoods or invert covariance matrices, and c) even for this simple example, implicit, simulation-based likelihood incurs a much smaller computational cost than inference with an explicit likelihood. This work uses a new IMNNs implementation in $\texttt{Jax}$ that can take advantage of fully-differentiable simulation and inference pipeline. We also demonstrate that a single retraining of the IMNN summaries effectively achieves the theoretically maximal information, enhancing the robustness to the choice of fiducial model where the IMNN is trained.