# Generalized Information Criteria for Structured Sparse Models

arXiv: https://arxiv.org/abs/2309.01764 · HTML: https://mlsanity.com/paper/2309.01764/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 34 references that are in the map.
- First posted on arXiv 4 Sep 2023.

## Builds on (most cited first, 1 of 1)

- [On Cross-validation for Sparse Reduced Rank Regression](https://mlsanity.com/paper/1812.11555/) (2018)

## Abstract (arXiv)

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.