On graphical models and convex geometry

被引：2

作者：

Bar, Haim ^{[1
]}

Wells, Martin T. ^{[2
]}

机构：

[1] Univ Connecticut, Dept Stat, Room 315,Philip E Austin Bldg, Storrs, CT 06269 USA

[2] Cornell Univ, Dept Stat & Data Sci, 1190 Comstock Hall, Ithaca, NY 14853 USA

来源：

COMPUTATIONAL STATISTICS & DATA ANALYSIS | 2023年 / 187卷

关键词：

Convex geometry; Correlation matrix estimation; Expectation Maximization (EM) algorithm; Graphical models; Grassmann manifold; High-dimensional inference; Network models; Phase transition; Quasi-orthogonality; Two-group model; COVARIANCE MATRICES; MAXIMUM-LIKELIHOOD; CONFIDENCE-REGIONS; SPARSE REGRESSION; SELECTION; DISTRIBUTIONS; REGULARIZATION; COHERENCE; INFERENCE; RECOVERY;

D O I：

10.1016/j.csda.2023.107800

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

A mixture-model of beta distributions framework is introduced to identify significant correlations among P features when P is large. The method relies on theorems in convex geometry, which are used to show how to control the error rate of edge detection in graphical models. The proposed 'betaMix' method does not require any assumptions about the network structure, nor does it assume that the network is sparse. The results hold for a wide class of data-generating distributions that include light-tailed and heavy-tailed spherically symmetric distributions. The results are robust for sufficiently large sample sizes and hold for non-elliptically-symmetric distributions. (c) 2023 Elsevier B.V. All rights reserved.

引用

页数：17

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