Pathwise Least Angle Regression and a Significance Test for the Elastic Net
Abstract
Least angle regression (LARS) by Efron et al. (2004) is a novel method for constructing the piecewise linear path of Lasso solutions. For several years, it remained also as the de facto method for computing the Lasso solution before more sophisticated optimization algorithms preceded it. LARS method has recently again increased its popularity due to its ability to find the values of the penalty parameters, called knots, at which a new parameter enters the active set of nonzero coefficients. Significance test for the Lasso by Lockhart et al. (2014), for example, requires solving the knots via the LARS algorithm. Elastic net (EN), on the other hand, is a highly popular extension of Lasso that uses a linear combination of Lasso and ridge regression penalties. In this paper, we propose a new novel algorithm, called pathwise (PW)LARSEN, that is able to compute the EN knots over a grid of EN tuning parameter {\alpha} values. The developed PWLARSEN algorithm decreases the EN tuning parameter and exploits the previously found knot values and the original LARS algorithm. A covariance test statistic for the Lasso is then generalized to the EN for testing the significance of the predictors. Our simulation studies validate the fact that the test statistic has an asymptotic Exp(1) distribution.
 Publication:

arXiv eprints
 Pub Date:
 June 2017
 arXiv:
 arXiv:1706.07511
 Bibcode:
 2017arXiv170607511N
 Keywords:

 Statistics  Methodology;
 Mathematics  Optimization and Control
 EPrint:
 5 pages, 25th European Signal Processing Conference (EUSIPCO 2017)