A Bridge between Invariant Theory and Maximum Likelihood Estimation

IF 12.7 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

ACS Central Science Pub Date : 2024-11-07 DOI:10.1137/24m1661753

Carlos Améndola, Kathlén Kohn, Philipp Reichenbach, Anna Seigal

引用次数: 0

Abstract

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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不变量理论与最大似然估计之间的桥梁

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

ACS Central Science Chemical Engineering-General Chemical Engineering

CiteScore

25.50

自引率

0.50%

发文量

194

审稿时长

10 weeks

期刊介绍： ACS Central Science publishes significant primary reports on research in chemistry and allied fields where chemical approaches are pivotal. As the first fully open-access journal by the American Chemical Society, it covers compelling and important contributions to the broad chemistry and scientific community. "Central science," a term popularized nearly 40 years ago, emphasizes chemistry's central role in connecting physical and life sciences, and fundamental sciences with applied disciplines like medicine and engineering. The journal focuses on exceptional quality articles, addressing advances in fundamental chemistry and interdisciplinary research.