Title: A Fast and Scalable Pathwise-Solver for Group Lasso and Elastic Net Penalized Regression via Block-Coordinate Descent

Abstract: We develop fast and scalable algorithms based on block-coordinate descent to solve the group lasso and the group elastic net for generalized linear models along a regularization path. Special attention is given when the loss is the usual least squares loss (Gaussian loss). We show that each block-coordinate update can be solved efficiently using Newton's method and further improved using an adaptive bisection method, solving these updates with a quadratic convergence rate. Our benchmarks show that our package adelie performs 3 to 10 times faster than the next fastest package on a wide array of both simulated and real datasets. Moreover, we demonstrate that our package is a competitive lasso solver as well, matching the performance of the popular lasso package glmnet.