Beyond Lasso: Dealing with Correlated Predictors, etc.

 

Hierarchical Variable Selection

  1. Nicolai Meinshausen (2008). Hierarchical testing of variable importance. Biometrika 95(2), 265-278
    If there is not enough information to distinguish reliably between highly correlated predictors in variable selection, this hierarchical algorithm can still detect important clusters of variables.

Fused Lasso

  1. Robert Tibshirani, Michael Saunders, Saharon Rosset, and Ji Zhu. Sparsity and smoothness via the fused lasso.  Published in J. Royal. Statist. Soc. B. 
  2. Rob Tibshirani and Pei Wang. Spatial smoothing and hot spot detection for CGH data using the Fused Lasso. To appear, Biostatistics. 
  3. Jerome Friedman, Trevor Hastie, Holger Hoefling and Robert Tibshirani, Pathwise Coordinate Optimization.  (shows how coordinate descent algorithms can efficiently solve a number of popular regularized optimization problems, creating an entire path of solutions; generalizes this approach to derive an efficient algorithm for the fused lasso, both one- and two-dimensional). Annals of Applied Statistics (2007), 1(2), 302-332.

Group  Lasso

  1. Ming Yuan, Yi Lin (2006). Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 68 (1) , 49–67   

  2. F. Bach,  Consistency of the group lasso and multiple kernel learning, Technical report HAL-00164735, 2008, to appear in Journal of Machine Learning Research

Simultaneous  Lasso

  1. J. A. Tropp, A. C. Gilbert, and M. J. Strauss. Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit. Signal Processing, special issue "Sparse approximations in signal and image processing," vol. 86, pp. 572-588, Apr. 2006. Preprint: [ .pdf ]
  2. J. A. Tropp. Algorithms for simultaneous sparse approximation. Part II: Convex relaxation". Signal Processing, special issue "Sparse approximations in signal and image processing," vol. 86, pp. 589-602, Apr. 2006. Preprint: [ .pdf ]
  3. B. Turlach et al. Simultaneous Variable Selection

Adaptive Lasso

  1.  Hui  Zou. The Adaptive Lasso and Its Oracle Properties. Journal of the American Statistical Association, 2006, vol. 101, pages 1418-1429

  2. Jian Huang, Shuangge Ma, and Cun-Hui Zhang. ADAPTIVE LASSO FOR SPARSE HIGH-DIMENSIONAL REGRESSION MODELS 
  3. Hao Helen Zhang and Wenbin Lu. Adaptive Lasso for Cox's proportional hazards model

Smoothed  Lasso

  1. http://stat.ethz.ch/talks/Ascona_07/Slides/meier.pdf