Open Access
2023 Deviance matrix factorization
Liang Wang, Luis Carvalho
Author Affiliations +
Electron. J. Statist. 17(2): 3762-3810 (2023). DOI: 10.1214/23-EJS2174


We investigate a general matrix factorization for deviance-based data losses, extending the ubiquitous singular value decomposition beyond squared error loss. While similar approaches have been explored before, our method leverages classical statistical methodology from generalized linear models (GLMs) and provides an efficient algorithm that is flexible enough to allow for structural zeros via entry weights. Moreover, by adapting results from GLM theory, we provide support for these decompositions by (i) showing strong consistency under the GLM setup, (ii) checking the adequacy of a chosen exponential family via a generalized Hosmer-Lemeshow test, and (iii) determining the rank of the decomposition via a maximum eigenvalue gap method. To further support our findings, we conduct simulation studies to assess robustness to decomposition assumptions and extensive case studies using benchmark datasets from image face recognition, natural language processing, network analysis, and biomedical studies. Our theoretical and empirical results indicate that the proposed decomposition is more flexible, general, and robust, and can thus provide improved performance when compared to similar methods. To facilitate applications, an R package dmf with efficient model fitting and family and rank determination is also provided.


We thank two anonymous referees and the associate editor who provided many valuable comments that significantly improved the paper. We also thank Weixuan Xia who provided suggestions and validation on our consistency proof.


Download Citation

Liang Wang. Luis Carvalho. "Deviance matrix factorization." Electron. J. Statist. 17 (2) 3762 - 3810, 2023.


Received: 1 January 2022; Published: 2023
First available in Project Euclid: 11 December 2023

Digital Object Identifier: 10.1214/23-EJS2174

Keywords: factor models , Non-negative matrix factorization , Principal Component Analysis

Vol.17 • No. 2 • 2023
Back to Top