Fr’echet regression for multi-label feature selection with implicit regularization
arXiv:2412.18247v1 Announce Type: new
Abstract: Fr’echet regression extends linear regression to model complex responses
in metric spaces, making it particularly relevant for multi-label regression,
where each instance can have multiple associated labels. However, variable
selection within this framework remains underexplored. In this paper, we pro pose a novel variable selection method that employs implicit regularization
instead of traditional explicit regularization approaches, which can introduce
bias. Our method effectively captures nonlinear interactions between predic tors and responses while promoting model sparsity. We provide theoretical
results demonstrating selection consistency and illustrate the performance of
our approach through numerical examples
Abstract: Fr’echet regression extends linear regression to model complex responses
in metric spaces, making it particularly relevant for multi-label regression,
where each instance can have multiple associated labels. However, variable
selection within this framework remains underexplored. In this paper, we pro pose a novel variable selection method that employs implicit regularization
instead of traditional explicit regularization approaches, which can introduce
bias. Our method effectively captures nonlinear interactions between predic tors and responses while promoting model sparsity. We provide theoretical
results demonstrating selection consistency and illustrate the performance of
our approach through numerical examples
Dou El Kefel Mansouri, Seif-Eddine Benkabou, Khalid Benabdeslem
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