The Lasso Page

L1-constrained fitting
for statistics and data mining

The Lasso is a shrinkage and selection method for linear regression. It minimizes the usual sum of squared errors, with a bound on the sum of the absolute values of the coefficients. It has connections to soft-thresholding of wavelet coefficients, forward stagewise regression, and boosting methods.

A simple explanation of the lasso and least angle regression

Lasso resources and links

The original lasso paper:

Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. J. Royal. Statist. Soc B., Vol. 58, No. 1, pages 267-288).
Global matched filtering in Engineering:

J.J. Fuchs. On the application of the global matched filter to DOA estimation with uniform circular arrays. IEEE Trans, S.P., vol.49, p.702--709, apr. 2001.
The least angle regression (LAR) algorithm for solving the Lasso:

Efron, B., Johnstone, I., Hastie, T. and Tibshirani, R. (2002). Least angle regression pdf file. Published in Annals of Statistics 2003

LARS software for Splus and R. The software computes the entire LAR, Lasso or Stagewise path in the same order of computations as a single least-squares fit.
The glmnet package for fitting Lasso and elastic net models can be found on CRAN . Here is a MATLAB version .
L1-constraints for non-orthogonal wavelet expansions:

Chen, Donoho, and Saunders: "Atomic Decomposition by Basis Pursuit(ps file)" (pdf)
Survival analysis: Tibshirani, R. (1997). The lasso method for variable selection in the Cox model. Statistics in Medicine 1998
M. Osborne, B. Presnell, and B. Turlach: Research and software for the Lasso: Their page at Univ. of Western Australia
Algorithms (the "Shooting" method) Wenjiang Fu (1998). Penalized regressions: the bridge vs the lasso. JCGS vol 7, no. 3, 397-416.
Asymptotics: Keith Knight and Wenjiang Fu (2000). Asymptotics for lasso-type estimators Ann. Statist. 28, no. 5, 1356--1378
Books describing the lasso:

Elements of Statistical Learning:
data mining, inference and prediction (Hastie, Tibshirani ,Friedman)

Subset selection in regression (Miller)