Weakly decomposable regularization penalties and structured sparsity
By Sara A. van de Geer. 2012
63 citations recorded by the source corpus.
It has been shown in literature that the Lasso estimator, or ℓ1‐penalized least squares estimator, enjoys good oracle properties. This paper examines which special properties of the ℓ1‐penalty allow for sharp oracle results, and then extends the situation to general norm‐based penalties that satisfy a weak decomposability condition.
Subfields: Computational Mechanics, Epidemiology, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/872b6981202f82b56961ef5226a476038b232fad
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In Computational Mechanics
In Epidemiology
In Statistics and Probability
Citations in the corpus
- Group Regularized Estimation Under Structural Hierarchy (2014, unknown): “…)〉 ≤ ‖X̄ ε‖∞‖ ‖1 and 〈ε, X̆ vec ( )〉 ≤ ‖X̆ ε‖2,∞‖ ‖2,1 as commonly used in the literature (Bickel, Ritov, and Tsybakov 2009; Lounici et al. 2011; Negahban et al. 2012; van de Geer 2014) would yield a prediction error bound of the order σ 2(Je log p+ JGp), which is, ironically,muchworse than the…”
- Robust machine learning by median-of-means: Theory and practice (2017, result): “This was shown for example, in [14, 58, 93, 94, 65, 72, 90] for estimation and sparse oracle inequalities, in [64, 99, 6] for support recovery results; more results and references on LASSO can be found in the books [19, 44].”