Coordinate descent algorithms for lasso penalized regression

Imposition of a lasso penalty shrinks parameter estimates toward zero and performs continuous model selection. Lasso penalized regression is capable of handling linear regression problems where the number of predictors far exceeds the number of cases. This paper tests two exceptionally fast algorithms for estimating regression coefficients with a lasso penalty. The previously known ℓ2 algorithm is based on cyclic coordinate descent. Our new ℓ1 algorithm is based on greedy coordinate descent and Edgeworth’s algorithm for ordinary ℓ1 regression. Each algorithm relies on a tuning constant that can be chosen by cross-validation. In some regression problems it is natural to group parameters and penalize parameters…