On graphical models and convex geometry

Haim Bar and Martin T. Wells

Computational Statistics & Data Analysis, 2023, vol. 187, issue C

Abstract: 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.

Keywords: 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 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:187:y:2023:i:c:s0167947323001111

DOI: 10.1016/j.csda.2023.107800

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