A NOTE ON THE LASSO AND RELATED PROCEDURES IN MODEL SELECTION

By Chenlei Leng, Yi Lin, Grace Wahba. 2006

335 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ef767b585b5d72e2194060060100d349b1f0486d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

The Adaptive Lasso and Its Oracle Properties (2006, background): “It is also interesting to note that when p 2, the necessary condition is always satisﬁed, because | C 21 − 1 11 sgn ∗ A | reduces to | | , the correlation between the two = = Given the facts”
L1-Norm Quantile Regression (2008, methodology): “(2004) and the kernel quantile regression (KQR) algorithm we have developed earlier in Li, Liu, and Zhu (2007), because we are now dealing with a nondifferentiable loss function and a nondifferentiable penalty.”
Discussion: A tale of three cousins: Lasso, L2Boosting and Dantzig (2007, background): “to include too many noise variables for low SNR – this is well-known and has already been studied in more detail in (Leng et al., 2006; Meinshausen and Bühlmann, 2006).”
ℓ1-regularized linear regression: persistence and oracle inequalities (2011, background): “The results can be divided into two categories: those that study the predictive power of β̂ [9, 30, 12] and those that study its sparsity pattern and reconstruction properties [4, 32, 18, 19, 17, 8]; this article falls into the first of these categories.”
Group Lasso with Overlaps: the Latent Group Lasso approach (2011, background): “We consider these two criteria since it is known that the regularization regime corresponding to optimal support recovery and best MSE are not the same (Bach, 2008b; Leng et al., 2004).”
LASSO Isotone for High-Dimensional Additive Isotonic Regression (2010, methodology): “In minimising predictive error, however, we do still ﬁt some irrelevant covariates as non-zero, a phenomenon previously observed with the LASSO in Leng et al. [2006].”
Adaptive Lasso for sparse high-dimensional regression models (2008, methodology): “We use the data set reported in Scheetz et al. (2006) to illustrate the application of the adaptive Lasso in high-dimensional settings.”
Asymptotic analysis of high-dimensional LAD regression with Lasso (2016, background): “Examples include Knight and Fu (2000); Greenshtein and Ritov (2004); Leng, Lin, and Wahba (2006); Meinshausen and Bühlmann (2006); Zhao and Yu (2006); Meinshausen and Yu (2009); van de Geer (2008); and Zhang and Huang (2008), among others.”
Regression coefficient and autoregressive order shrinkage and selection via the lasso (2007, methodology): “Note that the regression model (8) is adapted from Tibshirani (1996) and has been used in other simulation studies (e.g., see Fan and Li, 2001; Zou et al., 2005; Leng et al., 2005), while the autoregression model (9) is modified from Shi and Tsai (2004).”
On Model Selection Consistency of Lasso (2006, result): “After we had obtained our almost necessary and sufficient condition result, it was brought to our attention of an independent result in Meinshausen and Buhlmann (2006) where a similar condition to the Irrepresentable Condition was obtained to prove a model selection consistency result for Gaussian g”
On the distribution of the adaptive LASSO estimator (2008, unknown): “[This is in line with theoretical results in Leng et al. (2006), see also Leeb & Pötscher (2008b).] In agreement with the theoretical results in Section 3.”
High-dimensional regression with unknown variance (2011, result): “, take λ = λ∗ as defined in (4)], the lasso is not consistent for support estimation; see [51, 56] for results in a random design setting.”
Unified LASSO Estimation by Least Squares Approximation (2007, methodology): “…by a number of authors, because the traditional LASSO uses the same amount of shrinkage for each regression coefficient, the resulting estimator cannot be as efficient as the oracle (Fan and Li 2001), and the selection results can be inconsistent (Leng et al. 2006; Zou 2006; Yuan and Lin 2007).”