Generalized Information Criteria for Structured Sparse Models
Abstract
Regularized m-estimators are widely used due to their ability of recovering a low-dimensional model in high-dimensional scenarios. Some recent efforts on this subject focused on creating a unified framework for establishing oracle bounds, and deriving conditions for support recovery. Under this same framework, we propose a new Generalized Information Criteria (GIC) that takes into consideration the sparsity pattern one wishes to recover. We obtain non-asymptotic model selection bounds and sufficient conditions for model selection consistency of the GIC. Furthermore, we show that the GIC can also be used for selecting the regularization parameter within a regularized -estimation framework, which allows practical use of the GIC for model selection in high-dimensional scenarios. We provide examples of group LASSO in the context of generalized linear regression and low rank matrix regression.
Cite
@article{arxiv.2309.01764,
title = {Generalized Information Criteria for Structured Sparse Models},
author = {Eduardo F. Mendes and Gabriel J. P. Pinto},
journal= {arXiv preprint arXiv:2309.01764},
year = {2023}
}