Speaker
Description
We propose a novel sparsity enhancement strategy for regression tasks, based on learning a data-adaptive kernel metric, i.e., a shape matrix, through 2-Layered kernel machines [2]. The resulting shape matrix, which defines a Mahalanobis-type deformation of the input space, is then decomposed via Singular Value Decomposition (SVD), allowing us to identify the most informative directions. This task-aware approach provides a flexible, interpretable, and accurate feature reduction scheme. Numerical experiments on both synthetic and real-world datasets demonstrate that our approach achieves minimal yet highly informative feature sets without loosing predictive performances. We further consider an application within the field of solar physics, focusing on the prediction of a geomagnetic storms [1].
[1] F. Camattari, S. Guastavino, F. Marchetti, M. Piana, E. Perracchione, Classifier-dependent feature selection via greedy methods, Stat Comput, 34 (2024), 151
[2] T. Wenzel, F. Marchetti, E. Perracchione, Data-Driven Kernel Designs for Optimized Greedy Schemes: A Machine Learning Perspective, SIAM J. Sci. Comput., 46 (2024), no. 1, C101-C126
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