Learning permutation symmetries with gips in R

Abstract: The study of hidden structures in data presents challenges in modern statistics and machine learning. We introduce the $\mathbf{gips}$ package in R, which identifies permutation subgroup symmetries in Gaussian vectors. $\mathbf{gips}$ serves two main purposes: exploratory analysis in discovering hidden permutation symmetries and estimating the covariance matrix under permutation symmetry. It is competitive to canonical methods in dimensionality reduction while providing a new interpretation of the results. $\mathbf{gips}$ implements a novel Bayesian model selection procedure within Gaussian vectors invariant under the permutation subgroup introduced in Graczyk, Ishi, Ko{\l}odziejek, Massam, Annals of Statistics, 50 (3) (2022).