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.

我们提出了一种快速方法来解决压缩感知、Lasso回归和逻辑回归问题，通过使用主动集方法迭代运行适当的解算器。我们设计了一种更新主动集的策略，相对于单个调用多个解算器，包括稀疏重构的梯度投影（GPSR）、Matlab的lassoglm和glmnet，实现了大幅加速。对于压缩感知问题，我们的方法与GPSR的混合平均速度提升为Gaussian合奏的31.41倍，二元合奏的平均速度提升为25.64倍。在我们的实验中，对于Lasso回归，我们的方法与GPSR的混合平均速度提升为30.67倍。在我们的逻辑回归实验中，我们的方法与lassoglm的混合平均速度提升为11.95倍，与glmnet的混合平均速度提升为1.40倍。

Lasso和Logistic Lasso的快速方法