# Generalized Matrix Factorization: efficient algorithms for fitting generalized linear latent variable models to large data arrays

arXiv: https://arxiv.org/abs/2010.02469 · HTML: https://mlsanity.com/paper/2010.02469/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2020.

## Built on by (most cited first, 4 of 4)

- [Efficient Alternating Minimization with Applications to Weighted Low Rank Approximation](https://mlsanity.com/paper/2306.04169/) (2023)
- [Weighted Low-Rank Matrix Approximation: Acceleration and Applications](https://mlsanity.com/paper/2109.11057/) (2021)
- [Reweighted Solutions for Weighted Low Rank Approximation](https://mlsanity.com/paper/2406.02431/) (2024)
- [Stochastic gradient descent estimation of generalized matrix factorization models with application to single-cell RNA sequencing data](https://mlsanity.com/paper/2412.20509/) (2024)

## Abstract (arXiv)

Unmeasured or latent variables are often the cause of correlations between multivariate measurements, which are studied in a variety of fields such as psychology, ecology, and medicine. For Gaussian measurements, there are classical tools such as factor analysis or principal component analysis with a well-established theory and fast algorithms. Generalized Linear Latent Variable models (GLLVMs) generalize such factor models to non-Gaussian responses. However, current algorithms for estimating model parameters in GLLVMs require intensive computation and do not scale to large datasets with thousands of observational units or responses. In this article, we propose a new approach for fitting GLLVMs to high-dimensional datasets, based on approximating the model using penalized quasi-likelihood and then using a Newton method and Fisher scoring to learn the model parameters. Computationally, our method is noticeably faster and more stable, enabling GLLVM fits to much larger matrices than previously possible. We apply our method on a dataset of 48,000 observational units with over 2,000 observed species in each unit and find that most of the variability can be explained with a handful of factors. We publish an easy-to-use implementation of our proposed fitting algorithm.