Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties

By Jianqing Fan, Runze Li. 2001

9,697 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistics and Probability, Optimization & Training

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Citations in the corpus

Extended Comparisons of Best Subset Selection, Forward Stepwise Selection, and the Lasso (2017, neutral): “, 1994); nonconvex-penalized methods, such as SCAD (Fan and Li, 2001), MC+ (Zhang, 2010), and SparseNet (Mazumder et al.”
Best Subset Selection via a Modern Optimization Lens (2015, methodology): “…regression is often used to “bridge” the gap between the convex 1 penalty and the combinatorial 0 penalty [Candès, Wakin and Boyd (2008), Fan and Li (2001), Frank and Friedman (1993), Friedman (2008), Mazumder, Friedman and Hastie (2011), Zhang (2010a, 2010b), Zhang and Huang (2008), Zou…”
Spectral Regularization Algorithms for Learning Large Incomplete Matrices (2010, background): “See [Fri08, FL01 , Zha07] for examples of such penalties.”
Regularization Paths for Generalized Linear Models via Coordinate Descent (2010, methodology): “Methods using non-concave penalties, such as SCAD (Fan and Li 2005) and Friedman’s generalized elastic net (Friedman 2008), enforce more severe variable selection than the lasso.”
Optimization with Sparsity-Inducing Penalties (2011, background): “Other nonconvex regularization functions have been proposed in the statistics community, such as the SCAD penalty [43].”
Nearly unbiased variable selection under minimax concave penalty (2010, background): “Prior to the above mentioned studies about the interference of the bias of the LASSO with accurate variable selection or conditions to limit such interference, Fan and Li (2001) raised the concern of the effect of the bias of more general penalized estimators on estimation efficiency.”
On Nonconvex Decentralized Gradient Descent (2016, background): “Besides q quasi-norm, there are some other typical cases like SCAD [16] and MCP [68] widely used in statistical learning, satisfying the condition (c) of this theorem.”
Accelerated gradient methods for nonconvex nonlinear and stochastic programming (2013, background): “, [7,21]) consist of both convex and nonconvex components, corresponding to the data fidelity and sparsity regularization terms respectively.”
PERFORMANCE GUARANTEES FOR INDIVIDUALIZED TREATMENT RULES (2011, methodology): “In fact, many other penalization methods such as SCAD [9] and l1 penalty with adaptive weights (adaptive Lasso; [37]) also have this property.”
Compressing Neural Networks using the Variational Information Bottleneck (2018, background): “This is because the ‘ 1 norm tends to over-shrink large coeﬃcients at the expense of sparsity (Fan & Li, 2001).”
Distributed Sparse Linear Regression (2010, background): “Those include not only the bias, but also weak support consistency as well as estimation consistency, which for the centralized Lasso have been studied in, e.g., [39] and [11].”
Estimating brain functional connectivity with sparse multivariate autoregression (2005, methodology): “Of particular interest is recent work in the use of penalized regression methods for existing variable selection (Fan & Li 2001; Fan & Peng 2004) which unify nearly all variable selection techniques into an easy-to-implement iterative application of minimum norm or structure.”