Generalized Information Criteria for Structured Sparse Models
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...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
04.09.2023
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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DOI: | 10.48550/arxiv.2309.01764 |