Learning permutation symmetries with gips in R

TL;DR

The paper introduces the gips package in R for identifying permutation symmetries in Gaussian data, aiding exploratory analysis and covariance estimation, with competitive dimensionality reduction and new interpretability.

Contribution

It presents a novel Bayesian model selection method for permutation symmetries in Gaussian vectors, implemented in the gips package.

Findings

gips effectively detects permutation symmetries in Gaussian data

Provides competitive dimensionality reduction compared to canonical methods

Offers new interpretability for symmetry-based covariance estimation

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).