Accelerated structured matrix factorization
- URL: http://arxiv.org/abs/2212.06504v1
- Date: Tue, 13 Dec 2022 11:35:01 GMT
- Title: Accelerated structured matrix factorization
- Authors: Lorenzo Schiavon, Bernardo Nipoti, Antonio Canale
- Abstract summary: Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures.
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.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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