Accelerated structured matrix factorization
in: Journal of Computational and Graphical Statistics, 2024.
Citation: Schiavon, L., Nipoti, B., Canale, A. (2024) Accelerated structured matrix factorization, in Journal of Computational and Graphical Statistics, 33 (3), 917–927. doi: 10.1080/10618600.2023.2301072
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 interpretation 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 a 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. Supplemental materials are available online.