论文标题
最大似然估计的不变理论和缩放算法
Invariant theory and scaling algorithms for maximum likelihood estimation
论文作者
论文摘要
我们发现统计中最大似然估计与不变理论中的组轨道的最小化之间的联系。我们专注于高斯转化家族，其中包括矩阵正常模型和通过及当定向无环图给出的高斯图形模型。我们在小组行动下使用稳定性来表征最大似然估计的可能性的界限，存在和独特性。我们的方法揭示了不变理论与统计学之间相互作用的有希望的后果。特别是，现有的统计算法可以在不变理论中使用，反之亦然。
We uncover connections between maximum likelihood estimation in statistics and norm minimization over a group orbit in invariant theory. We focus on Gaussian transformation families, which include matrix normal models and Gaussian graphical models given by transitive directed acyclic graphs. We use stability under group actions to characterize boundedness of the likelihood, and existence and uniqueness of the maximum likelihood estimate. Our approach reveals promising consequences of the interplay between invariant theory and statistics. In particular, existing scaling algorithms from statistics can be used in invariant theory, and vice versa.
