Adaptive Lasso for sparse high-dimensional regression models

By Jian Huang, Shuangge Ma, Cun-Hui Zhang. 2008

672 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/5f0d051ffcbde45f92daee6395883cd476777ad9

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Citations in the corpus

Asymptotic Properties of Lasso+mLS and Lasso+Ridge in Sparse High-dimensional Linear Regression (2013, methodology): “Our analysis is not limited to adopting the Lasso in the selection stage, but is applicable to any other model selection criteria with exponentially decay rates of the probability of selecting wrong models, for example, stability selection [38], SCAD [21, 34] and Dantzig selector [12, 9, 26].”
SparseNet: Coordinate Descent With Nonconvex Penalties (2011, background): “The importance of the initial choice in obtaining “optimal” estimates via the re-weighted 1 minimization has also been pointed out in an asymptotic setting by Huang et al. (2008); our observations are non-asymptotic.”
Confidence intervals for low dimensional parameters in high dimensional linear models (2011, methodology): “…methods (Frank and Friedman, 1993; Fan and Li, 2001; Fan and Peng, 2004; Kim et al., 2008; Zhang, 2010; Zhang and Zhang, 2012), greedy methods (Zhang, 2011a), adaptive methods (Zou, 2006; Huang et al., 2008; Zhang, 2011b; Zhang and Zhang, 2012), screening methods (Fan and Lv, 2008), and more.”
Numerical construction of Green's functions in high dimensional elliptic problems with variable coefficients and analysis of renewable energy data via sparse and separable approximations (2012, methodology): “A similar idea, leading to the “adaptive lasso”, was developed in [78] under homoscedastic assumptions.”
ℓ1-penalization for mixture regression models (2010, background): “is then deﬁned as θˆ(γ) adapt;λ= argmin θ∈Θ −n−1ℓ(γ) adapt(θ), (14) where Θ is as in (11). The adaptive Lasso in linear models has better variable selection properties than the Lasso, see Zou (2006), Huang et al. (2008), van de Geer et al. (2010). We present some theory for the adaptive estimator in”
Shrinkage tuning parameter selection with a diverging number of parameters (2009, methodology): “Here d0 is allowed to be either fixed or diverging to ∞ as n→∞.”
The adaptive and the thresholded Lasso for potentially misspecified models (and a lower bound for the Lasso) (2011, background): “Further progress in the high-dimensional scenario has been achieved by [17].”
Forward Regression for Ultra-High Dimensional Variable Screening (2009, methodology): “Although the Adaptive LASSO is selection consistent under a general design condition (Zou, 2006; Zhang and Lu, 2007; Huang et al., 2007; Zou and Zhang, 2008; Zou and Li, 2008), it requires the sample size to be much larger than the predictor dimension.”
Boosting Algorithms: Regularization, Prediction and Model Fitting. Rejoinder. (2007, methodology): “Consistency of the adaptive Lasso for variable selection has been proved for the case with fixed predictordimension p [96] and also for the high-dimensional case with p = pn n [48].”
Review and evaluation of penalised regression methods for risk prediction in low‐dimensional data with few events (2015, methodology): “Huang et al [43] explored the use of adaptive lasso in microarray data and linear regression.”
Feature Selection for Classification: A Review (2014, unknown): “Complimentary to this proof, [24] shows that when m ≫ n for linear models, the adaptive Lasso estimate is also selection consistent under a partial orthogonality condition in which the covariates with zero coefficients are weakly correlated with the covariates with nonzero coefficients.”
Model confidence bounds for variable selection (2016, methodology): “model is m corresponds to coecients = (1;1;1;0;0;0). We generate B = 1000 bootstrap models selected by the adaptive lasso selection method with tuning constant selected by 10-fold cross-validation Huang et al. (2008). Figure 1 depicts all the possible models along with 90%-MCBs with the horizontal ”