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.

翻译：我们开发了基于块坐标下降的快速可扩展算法，用于沿正则化路径求解广义线性模型的组套索和组弹性网问题。特别关注损失函数为最小二乘损失（高斯损失）的情况。我们证明每个块坐标更新可通过牛顿法高效求解，并通过自适应二分法进一步改进，使这些更新达到二次收敛速度。基准测试表明，我们的软件包adelie在多种模拟和真实数据集上比次优软件包快3到10倍。此外，我们证明该软件包同样具备竞争力的套索求解能力，与流行套索软件包glmnet性能相当。