1. Accelerated Structured Matrix Factorization.
- Author
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Schiavon, Lorenzo, Nipoti, Bernardo, and Canale, Antonio
- Subjects
- *
MATRIX decomposition , *BOOSTING algorithms , *SIGNALS & signaling , *FACTORIZATION - 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 insights, 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 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. for this article are available online. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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