Cover It Up! Bipartite Graphs Uncover Identifiability in Sparse Factor Analysis

Darjus Hosszejni*, Sylvia Frühwirth-Schnatter

*Korrespondierende*r Autor*in für diese Arbeit

Publikation: Working/Discussion Paper

Abstract

Despite the popularity of factor models with sparse loading matrices, little attention has been given to formally address identifiability of these models beyond standard rotation-based identification such as the positive lower triangular constraint. To fill this gap, we present a counting rule on the number of nonzero factor loadings that is sufficient for achieving generic uniqueness of the variance decomposition in the factor representation. This is formalized in the framework of sparse matrix spaces and some classical elements from graph and network theory. Furthermore, we provide a computationally efficient tool for verifying the counting rule. Our methodology is illustrated for real data in the context of post-processing posterior draws in Bayesian sparse factor analysis.
OriginalspracheEnglisch
HerausgeberarXiv
Seiten1-20
Seitenumfang20
DOIs
PublikationsstatusVeröffentlicht - 1 Nov. 2022

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