A Fast Method for Lasso and Logistic Lasso
This work provides a faster solution for researchers and practitioners dealing with high-dimensional data in compressed sensing and regression tasks, but it is incremental as it builds on existing solvers with an active set strategy.
The paper tackles the problem of solving compressed sensing, Lasso regression, and Logistic Lasso regression more efficiently by proposing a fast method that uses an active set approach, achieving speedups of up to 31.41 times over existing solvers like GPSR.
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.