Learning Permutation Symmetry of a Gaussian Vector with gips in R

Abstract

The study of hidden structures in data presents challenges in modern statistics and machine learning. We introduce the gips package in R, which identifies permutation subgroup symmetries in Gaussian vectors. 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. gips implements a novel Bayesian model selection procedure within Gaussian vectors invariant under the permutation subgroup introduced in Graczyk, Ishi, Kołodziejek, and Massam (2022b, The Annals of Statistics).