论文标题
相关模型的可能性几何形状
Likelihood Geometry of Correlation Models
论文作者
论文摘要
相关矩阵是标准化的协方差矩阵。它们形成了通过将对角线条目设置为一个来定义的对称矩阵的仿射空间。我们研究了该模型的最大似然估计的几何形状以及编码其他对称性的线性子模型。我们还考虑了将协方差矩阵的两个密切相关功能最小化的问题：Stein的损失和对称的Stein的损失。与高斯对数模型不同，这两个功能是凸，因此承认具有独特的正定最佳最佳。我们的一些结果适用于一般仿射协方差模型。
Correlation matrices are standardized covariance matrices. They form an affine space of symmetric matrices defined by setting the diagonal entries to one. We study the geometry of maximum likelihood estimation for this model and linear submodels that encode additional symmetries. We also consider the problem of minimizing two closely related functions of the covariance matrix: the Stein's loss and the symmetrized Stein's loss. Unlike the Gaussian log-likelihood these two functions are convex and hence admit a unique positive definite optimum. Some of our results hold for general affine covariance models.
