On the non‐negative garrotte estimator

By Ming Yuan, Yi Lin. 2007

274 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/419c999432f38c89d4f40da5393832e73d937c89

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In Applied Mathematics

In Statistics and Probability

Citations in the corpus

Assumptionless consistency of the Lasso (2013, background): “[25], Knight and Fu [19], Fan and Li [15], Meinshausen and Bühlmann [23], Yuan and Lin [30], Zhao and Yu [33], Zou [34], Greenshtein and Ritov [17], Bunea et.”
Shrinkage inverse regression estimation for model‐free variable selection (2009, background): “As with the usual non-negative garrotte (see also a discussion in Yuan and Lin (2007)), the finite sample empirical performance of the shrinkage estimator relies on the initial estimator, which is the inverse regression estimator without shrinkage in our case.”
Stochastic and genetic neural network combinations in trading and hybrid time-varying leverage effects (2014, methodology): “Given the vectors of independent and dependent variables: and the training data {( X 1 ,y 1 ),…,( X N ,y N )} , the LASSO coefficients are estimated based on the following argument: The argument (8) is based on Breiman’s non-negative garrotte minimization process (Yuan and Lin, 2007).”
Variable selection for high-dimensional generalized varying-coefficient models (2012, background): “…has been made on the problem of variable selection for linear models and generalized linear models (Tibshirani (1996); Fan and Li (2001); Fan and Peng (2004); Zou (2006); Zou and Li (2008); Yuan and Lin (2007); Huang, Horowitz, and Ma (2008); Choi, Li, and Zhu (2010); Li, Peng, and Zhu (2011)).”
Self-concordant analysis for logistic regression (2009, result): “In Section 5, we consider regularizatio n by thel1-norm and extend two known recent results for the square loss, one on model consis te cy [12, 13, 14, 15] and one on prediction efficiency [16].”
Heterogeneous Domain Adaptation for Multiple Classes (2014, background): “Specifically, let G = [g1,g2, · · · ,gdT ]⊤, by imposing l1-regularization on gi and non-negative constraints gi ≽ 0, the problem of learning G can be formulated as the following nonnegative LASSO problem [33, 30]:”
Exploring Large Feature Spaces with Hierarchical Multiple Kernel Learning (2008, unknown): “With these assumptions, we can follo w the approach of [18, 19, 20] : that is, if λn tends to zero faster than n−1/2, then the estimatêβ converges in probability to the generating β, and we have the expansion̂ β = β + λnγ̂ whereγ̂ is the solution of the following optimization problem, with δ = ∑ v∈W”
On the asymptotic properties of the group lasso estimator for linear models (2008, methodology): “Instead, Yuan and Lin (2006) propose to use the group-lasso penalty, which is a convex relaxation to the ℓ0 penalty based on the combination of the ℓ1 penalty over the number of subspaces with the ℓ2 penalty on the estimated coefficients of each subspace.”
Consistency of the group Lasso and multiple kernel learning (2007, unknown): “They are based on the piecewise linearity of the set of solutions as a function of the regularization parameter l n (Efron et al., 2004).”
Reliable estimation of prediction errors for QSAR models under model uncertainty using double cross-validation (2014, unknown): “Moreover, the model error can be calculated precisely as follows [58]:”
THE Mnet method for variable selection (2016, background): “Yuan and Lin (2007) obtained a result for Elastic net to select the true model in the classical settings when p is fixed.”
Regularization Parameter Selections via Generalized Information Criterion (2010, background): “Recently, more researchers applied penalized approaches to study variable selections (e.g., Park and Hastie 2007; Wang and Leng 2007; Yuan and Lin 2007; Zhang and Lu 2007; Li and Liang 2008).”
Structured sparsity through convex optimization (2011, background): “Support recovery condition (Zhao and Yu, 2006; Wainwright, 2009; Zou, 2006; Yuan and Lin, 2007): the Lasso is sign-consistent if and only if there are low correlations between relevant and irrelevant variables.”