Work

Algebraic Sparse Factor Analysis

Year: 2025

Type: article

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.

Source: SIAM Journal on Applied Algebra and Geometry

DOI: 10.1137/23m1626517

Authors: Mathias Drton, Alexandros Grosdos, Irem Portakal, Nils Sturma

Institutions: Munich Center for Machine Learning, Technical University of Munich, University of Augsburg, Max Planck Institute for Mathematics in the Sciences

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green