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On the LASSO and Its Dual

Michael R. Osborne, Brett Presnell and Berwin A. Turlach
Journal of Computational and Graphical Statistics
Vol. 9, No. 2 (Jun., 2000), pp. 319-337
DOI: 10.2307/1390657
Stable URL: http://www.jstor.org/stable/1390657
Page Count: 19
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On the LASSO and Its Dual
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Abstract

Proposed by Tibshirani, the least absolute shrinkage and selection operator (LASSO) estimates a vector of regression coefficients by minimizing the residual sum of squares subject to a constraint on the l1-norm of the coefficient vector. The LASSO estimator typically has one or more zero elements and thus shares characteristics of both shrinkage estimation and variable selection. In this article we treat the LASSO as a convex programming problem and derive its dual. Consideration of the primal and dual problems together leads to important new insights into the characteristics of the LASSO estimator and to an improved method for estimating its covariance matrix. Using these results we also develop an efficient algorithm for computing LASSO estimates which is usable even in cases where the number of regressors exceeds the number of observations. An S-Plus library based on this algorithm is available from StatLib.

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