# Accelerated structured matrix factorization

arXiv: https://arxiv.org/abs/2212.06504 · HTML: https://mlsanity.com/paper/2212.06504/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 42 references that are in the map.
- First posted on arXiv 13 Dec 2022.

## Builds on (most cited first, 8 of 8)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [On Mixed Memberships and Symmetric Nonnegative Matrix Factorizations](https://mlsanity.com/paper/1607.00084/) (2016)
- [Bayesian cumulative shrinkage for infinite factorizations](https://mlsanity.com/paper/1902.04349/) (2019)
- [Cold-start recommendations in Collective Matrix Factorization](https://mlsanity.com/paper/1809.00366/) (2018)
- [Generalized infinite factorization models](https://mlsanity.com/paper/2103.10333/) (2021)
- [Structured prior distributions for the covariance matrix in latent factor models](https://mlsanity.com/paper/2208.07831/) (2022)

## Abstract (arXiv)

Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse structures. Sparsity, in addition, is beneficial in terms of regularization and, thus, to avoid over-fitting. By exploiting Bayesian shrinkage priors, we devise a computationally convenient approach for high-dimensional matrix factorization. The dependence between row and column entities is modeled by inducing flexible sparse patterns within factors. The availability of external information is accounted for in such a way that structures are allowed while not imposed. Inspired by boosting algorithms, we pair the the proposed approach with a numerical strategy relying on a sequential inclusion and estimation of low-rank contributions, with data-driven stopping rule. Practical advantages of the proposed approach are demonstrated by means of a simulation study and the analysis of soccer heatmaps obtained from new generation tracking data.