Precision inference in the nonlinear regime of large-scale structure is fundamentally limited by the complexity of summary statistic distributions and the information loss inherent in conventional compression schemes. These challenges can be addressed through simulation-based inference (SBI) combined with information-theoretic optimization of summary statistics.
In the context of weak gravitational lensing, we construct an optimized set of summaries that jointly captures large- and small-scale information by combining power spectra with convolutional neural network (CNN)-based features. Applying conditional mutual information for compression yields a minimal set of just seven highly informative statistics.
Using these summaries, we perform a fully Bayesian SBI analysis of Dark Energy Survey (DES) cosmic shear data, obtaining precise constraints on the wCDM parameters S_8, \Omega_m, and w. Importantly, while machine learning is used to construct the summaries, the SBI framework ensures that inference remains statistically rigorous and agnostic to how the compression was achieved.