Accelerated structured matrix factorization

TL;DR

This paper introduces a fast Bayesian-based matrix factorization method that models sparse structures and external information, improving interpretability and regularization in high-dimensional data analysis.

Contribution

It presents a novel computational approach combining Bayesian shrinkage priors with a boosting-inspired sequential estimation strategy for structured matrix factorization.

Findings

Demonstrated improved interpretability with sparse factors

Showed effectiveness on simulated data

Applied successfully to soccer heatmap analysis

Abstract

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.