We propose a fast method for solving compressed sensing, Lasso regression, and Logistic Lasso regression problems that iteratively runs an appropriate solver using an active set approach. We design a strategy to update the active set that achieves a large speedup over a single call of several solvers, including gradient projection for sparse reconstruction (GPSR), lassoglm of Matlab, and glmnet. For compressed sensing, the hybrid of our method and GPSR is 31.41 times faster than GPSR on average for Gaussian ensembles and 25.64 faster on average for binary ensembles. For Lasso regression, the hybrid of our method and GPSR achieves a 30.67-fold average speedup in our experiments. In our experiments on Logistic Lasso regression, the hybrid of our method and lassoglm gives an 11.95-fold average speedup, and the hybrid of our method and glmnet gives a 1.40-fold average speedup.

翻译：我们提出了一种用于求解压缩感知、Lasso回归和逻辑Lasso回归问题的快速方法，该方法通过采用活动集策略迭代运行适当的求解器。我们设计了一种更新活动集的方法，与单独使用多种求解器（包括用于稀疏重建的梯度投影（GPSR）、Matlab的lassoglm以及glmnet）相比，可大幅提升速度。对于压缩感知，我们的方法与GPSR的混合方法在处理高斯系综时平均速度比单独GPSR快31.41倍，在处理二值系综时平均快25.64倍。对于Lasso回归，我们的方法与GPSR的混合方法在实验中实现了30.67倍的平均加速比。在逻辑Lasso回归实验中，我们的方法与lassoglm的混合方法获得了11.95倍的平均加速比，而与glmnet的混合方法实现了1.40倍的平均加速比。