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Generalized Information Criteria for Structured Sparse Models

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  • Eduardo F. Mendes
  • Gabriel J. P. Pinto

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 $m$-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.

Suggested Citation

  • Eduardo F. Mendes & Gabriel J. P. Pinto, 2023. "Generalized Information Criteria for Structured Sparse Models," Papers 2309.01764, arXiv.org.
    • Handle: RePEc:arx:papers:2309.01764
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    References listed on IDEAS

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