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).

翻译：数据中隐藏结构的研究给现代统计学和机器学习带来了挑战。我们介绍了R语言中的$\mathbf{gips}$包，该包用于识别高斯向量中的排列子群对称性。$\mathbf{gips}$主要有两个目的：一是探索性分析，用于发现隐藏的排列对称性；二是在排列对称性假设下估计协方差矩阵。该方法在降维方面与经典方法具有竞争力，同时提供了对结果的全新解释。$\mathbf{gips}$实现了一种新颖的贝叶斯模型选择程序，适用于在Graczyk、Ishi、Ko{\l}odziejek和Massam发表于《统计年鉴》2022年第50卷第3期的论文中所引入的、在排列子群下保持不变的高斯向量。