On Graphical Models and Convex Geometry

Haim Bar; Martin T Wells

doi:10.1016/j.csda.2023.107800

On Graphical Models and Convex Geometry

Comput Stat Data Anal. 2023 Nov:187:107800. doi: 10.1016/j.csda.2023.107800. Epub 2023 Jun 14.

Authors

Haim Bar¹, Martin T Wells²

Affiliations

¹ Department of Statistics, University of Connecticut, Room 315, Philip E. Austin Building, Storrs, 06269-4120, CT, USA.
² Department of Statistics and Data Science, Cornell University, 1190 Comstock Hall, Ithaca, 14853, NY, USA.

PMID: 37396752
PMCID: PMC10310290 (available on 2024-11-01)
DOI: 10.1016/j.csda.2023.107800

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.

Grants and funding

R01 GM135926/GM/NIGMS NIH HHS/United States