Seminar

Tongtong Wu

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 talk 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 group by group rather than separately. If the group penalty is proportional to the Euclidean norm of the parameters of the group, then it is possible to majorize the norm and reduce parameter estimation to L2 regression with a lasso penalty. Thus, the existing algorithm can be extended to novel settings. Each of the algorithms discussed is tested via either simulated or real data or both. The appendix proves that a greedy form of the L2 algorithm converges to the minimum value of the objective function.

Seminar Date:
October 27, 2008