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

Darjus Hosszejni, Sylvia Frühwirth-Schnatter

arXiv 1 Nov 2022 · Econometrics · publishedJournal of Multivariate Analysis (2025) · 3 citations (OpenAlex)

arXiv:2211.00671 · PDF · DOI · OpenAlex · Extracted main text

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.

Citation extraction

32
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84
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appendix boundary found by appendix_titled_section at “Appendix\label{sec:appendix}” · 96% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1T. W. Anderson, H. Rubin, Statistical inference in factor analysis,… (1956) Statistical inference in factor analysis1.000103100%
2S. Frühwirth-Schnatter, D. Hosszejni, H. F. Lopes, When it counts–Ec… (2023) When it counts–Econometric identification of the basic factor model based on GLT structures1.00083100%
3S. Frühwirth-Schnatter, D. Hosszejni, H. F. Lopes, Sparse Bayesian f… (2024) Sparse Bayesian factor analysis when the number of factors is unknown0.9416383%
4M. Sato, A study of an identification problem and substitute use of… (1992) A study of an identification problem and substitute use of principal component analysis in factor analysis0.87462100%
5Y. Tumura, M. Sato, On the identification in factor analysis, TRU Ma… (1980) On the identification in factor analysis0.87452100%
6S. Kaufmann, C. Schuhmacher, Bayesian estimation of sparse dynamic f… (2019) Bayesian estimation of sparse dynamic factor models with order-independent and ex-post identification0.81142100%
7Z. Ghahramani, T. L. Griffiths, P. Sollich, Bayesian nonparametric l… (2007) Bayesian nonparametric latent feature models (with discussion and rejoinder)0.73732100%
8S. Frühwirth-Schnatter, Generalized cumulative shrinkage process pri… (2023) Generalized cumulative shrinkage process priors with applications to sparse Bayesian factor analysis0.69361100%
9S. Legramanti, D. Durante, D. B. Dunson, Bayesian cumulative shrinka… (2020) Bayesian cumulative shrinkage for infinite factorizations0.64441100%
10A. Bhattacharya, D. B. Dunson, Sparse Bayesian infinite factor model… (2011) Sparse Bayesian infinite factor models0.64422100%

Showing the top 10 of 32 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1When it counts - Econometric identification of the basic factor model based on GLT structures0.64422
2Generalized Cumulative Shrinkage Process Priors with Applications to Sparse Bayesian Factor Analysis0.40511