GEOMAX: beyond linear compression for 3pt galaxy clustering statistics

TL;DR

GEOMAX is a novel non-linear compression algorithm for bispectrum measurements that significantly improves parameter constraints in galaxy clustering data, outperforming traditional methods and applicable to various cosmological probes.

Contribution

We introduce GEOMAX, a two-step non-linear compression method that maximizes Fisher information for bispectrum data, enhancing parameter estimation efficiency.

Findings

Reduces credible intervals for key parameters by over 50%.

Performs 15% better than existing compression methods on mock data.

Is flexible and lossless, suitable for diverse cosmological analyses.

Abstract

We present the GEOMAX algorithm and its Python implementation for a two-step compression of bispectrum measurements. The first step groups bispectra by the geometric properties of their arguments; the second step then maximises the Fisher information with respect to a chosen set of model parameters in each group. The algorithm only requires the derivatives of the data vector with respect to the parameters and a small number of mock data, producing an effective, non-linear compression. By applying GEOMAX to bispectrum monopole measurements from BOSS DR12 CMASS redshift-space galaxy clustering data, we reduce the $68\%$ credible intervals for the inferred parameters $\left(b_1,b_2,f,\sigma_8\right)$ by $\left(50.4\%,56.1\%,33.2\%,38.3\%\right)$ with respect to standard MCMC on the full data vector. We run the analysis and comparison between compression methods over one hundred galaxy mocks to test the statistical significance of the improvements. On average GEOMAX performs $\sim15\%$ better than geometrical or maximal linear compression alone and is consistent with being lossless. Given its flexibility, the GEOMAX approach has the potential to optimally exploit three-point statistics of various cosmological probes like weak lensing or line-intensity maps from current and future cosmological data-sets such as DESI, Euclid, PFS and SKA.