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Weakly decomposable regularization penalties and structured sparsity

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  • Sara Geer

Abstract

type="main" xml:id="sjos12032-abs-0001"> It has been shown in literature that the Lasso estimator, or ℓ 1 -penalized least squares estimator, enjoys good oracle properties. This paper examines which special properties of the ℓ 1 -penalty allow for sharp oracle results, and then extends the situation to general norm-based penalties that satisfy a weak decomposability condition.

Suggested Citation

  • Sara Geer, 2014. "Weakly decomposable regularization penalties and structured sparsity," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 72-86, March.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:1:p:72-86
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    File URL: http://hdl.handle.net/10.1111/sjos.12032
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    Cited by:

    1. Tung Duy Luu & Jalal Fadili & Christophe Chesneau, 2021. "Sampling from Non-smooth Distributions Through Langevin Diffusion," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1173-1201, December.
    2. Caner, Mehmet, 2023. "Generalized linear models with structured sparsity estimators," Journal of Econometrics, Elsevier, vol. 236(2).
    3. van de Geer, Sara, 2016. "Worst possible sub-directions in high-dimensional models," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 248-260.
    4. Tino Werner, 2022. "Asymptotic linear expansion of regularized M-estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 167-194, February.
    5. Guillaume Lecué & Mathieu Lerasle, 2017. "Robust machine learning by median-of-means : theory and practice," Working Papers 2017-32, Center for Research in Economics and Statistics.
    6. Umberto Amato & Anestis Antoniadis & Italia Feis & Irène Gijbels, 2022. "Penalized wavelet estimation and robust denoising for irregular spaced data," Computational Statistics, Springer, vol. 37(4), pages 1621-1651, September.
    7. Tung Duy Luu & Jalal Fadili & Christophe Chesneau, 2020. "Sharp oracle inequalities for low-complexity priors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 353-397, April.

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