# Deviance Matrix Factorization

arXiv: https://arxiv.org/abs/2110.05674 · HTML: https://mlsanity.com/paper/2110.05674/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 69 references that are in the map.
- First posted on arXiv 12 Oct 2021.

## Builds on (most cited first, 5 of 5)

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Estimating Number of Factors by Adjusted Eigenvalues Thresholding](https://mlsanity.com/paper/1909.10710/) (2019)
- [Fast Matrix Factorization with Non-Uniform Weights on Missing Data](https://mlsanity.com/paper/1811.04411/) (2018)
- [Recommendation from Raw Data with Adaptive Compound Poisson Factorization](https://mlsanity.com/paper/1905.13128/) (2019)
- [A Generalized Hosmer-Lemeshow Goodness-of-Fit Test for a Family of Generalized Linear Models](https://mlsanity.com/paper/2007.11049/) (2020)

## Built on by (most cited first, 5 of 5)

- [Comprehensive evaluation of Mal-API-2019 dataset by machine learning in malware detection](https://mlsanity.com/paper/2403.02232/) (2024)
- [Journey into Automation: Image-Derived Pavement Texture Extraction and Evaluation](https://mlsanity.com/paper/2501.02414/) (2025)
- [Laplacian Kernelized Bandit](https://mlsanity.com/paper/2601.00461/) (2026)
- [Multiclass ROC](https://mlsanity.com/paper/2404.13147/) (2024)
- [Hierarchical Multi-Stage BERT Fusion Framework with Dual Attention for Enhanced Cyberbullying Detection in Social Media](https://mlsanity.com/paper/2503.00342/) (2025)

## Abstract (arXiv)

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 with efficient model fitting and family and rank determination is also provided.