[Least Angle Regression]: Discussion

By David Madigan, Greg Ridgeway. 2004

392 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Statistics and Probability

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Citations in the corpus

Best Subset Selection via a Modern Optimization Lens (2015, methodology): “We considered the Diabetes dataset [Efron et al. (2004)] with all the second order interactions included in the model, which resulted in 64 predictors.”
Nearly unbiased variable selection under minimax concave penalty (2010, methodology): “In each step, the PLUS computes one line segment in its path between two turning points, and its computational cost is the same as the LARS [Efron et al. (2004)] per step.”
High-dimensional graphs and variable selection with the Lasso (2006, methodology): “It is wellknown that the Lasso,introduced by Tibshirani[16],and known as Basis Pursuit in the context ofwavelet regression [2],has a parsim onious property [11].”
Discussion: A tale of three cousins: Lasso, L2Boosting and Dantzig (2007, methodology): “[8]) more challenging and gives rise to jittery paths relative to Lasso and L2Boosting, as seen in the simulated example below.”
Piecewise linear regularized solution paths (2007, methodology): “The LAR-Lasso algorithm [4] is a simplified version of this algorithm since “knot crossing” events do not occur in the”
A Selective Overview of Variable Selection in High Dimensional Feature Space (2009, methodology): “We show in this section that the penalized likelihood (2) can be solved by a sequence of reweighted penalized L 1 -regression problems via local linear approximation (Zou and Li (2008)).”
Discussion: The Dantzig selector: Statistical estimation when p is much larger than n (2007, neutral): “The Annals of Statistics 2007, Vol. 35, No. 6, 2358–2364 DOI: 10.1214/009053607000000433 Main article DOI: 10.1214/009053606000001523 © Institute of Mathematical Statistics, 2007”
Feature Screening via Distance Correlation Learning (2012, neutral): “…smoothly clipped absolute deviation (SCAD) (Fan and Li 2001; Kim, Choi, and Oh 2008; Zou and Li 2008), the least angle regression (LARS) algorithm (Efron et al. 2004), the elastic net (Zou and Hastie 2005; Zou and Zhang 2009), the adaptive LASSO (Zou 2006), and the Dantzig selector (Candes and…”
VARIABLE SELECTION IN NONPARAMETRIC ADDITIVE MODELS (2010, methodology): “The ordinary Lasso estimates are computed using the Lars algorithms [Efron et al. (2004)].”
STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION (2012, methodology): “For certain learning problems, such as the LASSO penalized least squares, the solution paths are piecewise linear which allows one to employ a LARS-type algorithm to compute the entire solution path efficiently (Efron et al., 2004).”
Sequential selection procedures and false discovery rate control (2013, methodology): “Variable selection along a regression path This problem of FDR control for ordered hypotheses arises naturally when implementing selection by using a path-based regression algorithm; examples of such algorithms include forward stepwise regression (see Hocking (1976) for a review) and least angle reg”
On the “degrees of freedom” of the lasso (2007, neutral): “The Annals of Statistics 2007, Vol. 35, No. 5, 2173–2192 DOI: 10.1214/009053607000000127 © Institute of Mathematical Statistics, 2007”
Estimation of oblique structure via penalized likelihood factor analysis (2013, neutral): “In regression analysis, a number of researchers have proposed fast algorithms to obtain the entire solutions (e.g., Least angle regression, Efron et al. 2004; Coordinate descent algorithm, Friedman et al. 2007; Generalized path seeking, Friedman 2012).”
Covariance Estimation: The GLM and Regularization Perspectives (2011, background): “Such an approach will inherit many desirable computational and statistical properties of LASSO and its many improved variants (Efron et al., 2004; Rocha, Zhao and Yu, 2008; Fan and Lv, 2010, Section 3.5).”