Algebraic Sparse Factor Analysis

MCML Authors

Mathias Drton

Prof. Dr.

Core PI

Mathematical Statistics

Nils Sturma

Dr.

* Former Member

→ Group Mathias Drton
 Mathematical Statistics

Abstract

Factor analysis is a statistical technique that explains correlations among observed random variables with the help of a smaller number of unobserved factors. In traditional full factor analysis, each observed variable is influenced by every factor. However, many applications exhibit interesting sparsity patterns; that is, each observed variable only depends on a subset of the factors. In this paper, we study such sparse factor analysis models from an algebro-geometric perspective. Under mild conditions on the sparsity pattern, we examine the dimension of the set of covariance matrices that corresponds to a given model. Moreover, we study algebraic relations among the covariances in sparse two-factor models. In particular, we identify cases in which a Gröbner basis for these relations can be derived via a 2-delightful term order and join of toric ideals of graphs.

article DGP+25

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SIAM Journal on Applied Algebra and Geometry

9. Feb. 2025.

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Authors

M. Drton • A. Grosdos • I. Portakal • N. Sturma

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Links

DOI

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Research Area

 A1 | Statistical Foundations & Explainability