Eduardo F. Mendes, Gabriel J. P. Pinto
arXiv 4 Sep 2023 · Statistics — Methodology
arXiv:2309.01764 · PDF · DOI · OpenAlex · Extracted main text
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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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | M. J. Wainwright (2019) High-Dimensional Statistics: A Non-Asymptotic Viewpoint | 1.000 | 14 | 5 | 100% |
| 2 | S. N. Negahban, P. Ravikumar, M. J. Wainwright, and B. Yu (2012) A unified framework for high-dimensional analysis of $ m $-estimators with decomposable regularizers | 1.000 | 11 | 4 | 100% |
| 3 | Y. Kim and J.-J. Jeon (2016) Consistent model selection criteria for quadratically supported risks | 1.000 | 6 | 3 | 100% |
| 4 | J. Chen and Z. Chen (2012) Extended BIC for small-n-large-P sparse GLM | 0.737 | 3 | 2 | 100% |
| 5 | P. Bühlmann and S. Van De Geer (2011) Statistics for high-dimensional data: methods, theory and applications | 0.644 | 2 | 2 | 100% |
| 6 | Y. She and H. Tran (2019) On cross-validation for sparse reduced rank regression | 0.585 | 3 | 1 | 100% |
| 7 | H. Wang, B. Li, and C. Leng (2008) Shrinkage tuning parameter selection with a diverging number of parameters | 0.585 | 3 | 1 | 100% |
| 8 | Y. Zhang and X. Shen (2010) Model selection procedure for high-dimensional data | 0.585 | 3 | 1 | 100% |
| 9 | J. Chen and Z. Chen (2008) Extended Bayesian Information Criteria for Model Selection with Large Model Spaces model selection Extended Bayesian information… | 0.511 | 2 | 1 | 100% |
| 10 | X. Gao and P. X-K Song (2010) Composite Likelihood Bayesian Information Criteria for Model Selection in High-Dimensional Data | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 35 scored citations.