不变量理论与最大似然估计之间的桥梁

IF 10.8 1区数学 Q1 MATHEMATICS, APPLIED

SIAM Review Pub Date : 2024-11-07 DOI:10.1137/24m1661753

Carlos Améndola, Kathlén Kohn, Philipp Reichenbach, Anna Seigal

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引用次数: 0

摘要

SIAM Review》，第 66 卷第 4 期，第 721-747 页，2024 年 11 月。我们揭示了统计中的最大似然估计与不变理论中的群轨道上的规范最小化之间的联系。我们提出的词典将几何不变理论中的稳定性概念与最大似然估计的存在性和唯一性联系起来。我们的词典适用于离散和连续统计模型：我们讨论了对数线性模型和高斯模型，包括矩阵正态模型和有向高斯图形模型。我们的方法揭示了不变量理论与统计学之间相互作用的前景。例如，统计中的算法可以用于不变量理论，反之亦然。

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A Bridge between Invariant Theory and Maximum Likelihood Estimation

SIAM Review, Volume 66, Issue 4, Page 721-747, November 2024.
We uncover connections between maximum likelihood estimation in statistics and norm minimization over a group orbit in invariant theory. We present a dictionary that relates notions of stability from geometric invariant theory to the existence and uniqueness of a maximum likelihood estimate. Our dictionary holds for both discrete and continuous statistical models: we discuss log-linear models and Gaussian models, including matrix normal models and directed Gaussian graphical models. Our approach reveals promising consequences of the interplay between invariant theory and statistics. For instance, algorithms from statistics can be used in invariant theory, and vice versa.

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来源期刊

SIAM Review 数学-应用数学

CiteScore

16.90

自引率

0.00%

发文量

期刊介绍： Survey and Review feature papers that provide an integrative and current viewpoint on important topics in applied or computational mathematics and scientific computing. These papers aim to offer a comprehensive perspective on the subject matter. Research Spotlights publish concise research papers in applied and computational mathematics that are of interest to a wide range of readers in SIAM Review. The papers in this section present innovative ideas that are clearly explained and motivated. They stand out from regular publications in specific SIAM journals due to their accessibility and potential for widespread and long-lasting influence.