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。