Group symmetry and covariance regularization
Group symmetry and covariance regularization
复制标题
群对称性和协方差正则化
DOI：
10.1109/ciss.2012.6310765
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
V. Chandrasekaran
中科院分区：
文献类型：
--
作者：
P. Shah;V. Chandrasekaran
具有对称性的统计模型出现在不同的环境中，例如与地球物理现象相关的随机场、贝叶斯统计中的可交换过程以及工程中的循环平稳过程。我们通过群不变性形式化对称模型的概念。我们提出投影到群不动点子空间作为高维体系中正则化协方差矩阵的基本方法。就与组相关的参数而言，我们得出正则化协方差矩阵的精确收敛率，并证明在样本复杂性方面可以预期显着的统计收益。
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the notion of a symmetric model via group invariance. We propose projection onto a group fixed point subspace as a fundamental way of regularizing covariance matrices in the high-dimensional regime. In terms of parameters associated to the group we derive precise rates of convergence of the regularized covariance matrix and demonstrate that significant statistical gains may be expected in terms of the sample complexity.