Safe Active Feature Selection for Sparse Learning
This work addresses scalability issues in sparse learning for researchers and practitioners dealing with extremely high-dimensional datasets, offering a safe and efficient alternative to existing screening methods.
The paper tackles the computational inefficiency of LASSO solutions for high-dimensional data by introducing SAIF, a safe active incremental feature selection method that starts with a small feature set and incrementally updates the model, achieving up to 50 times faster performance than dynamic screening and hundreds of times faster than standard methods without screening.
We present safe active incremental feature selection~(SAIF) to scale up the computation of LASSO solutions. SAIF does not require a solution from a heavier penalty parameter as in sequential screening or updating the full model for each iteration as in dynamic screening. Different from these existing screening methods, SAIF starts from a small number of features and incrementally recruits active features and updates the significantly reduced model. Hence, it is much more computationally efficient and scalable with the number of features. More critically, SAIF has the safe guarantee as it has the convergence guarantee to the optimal solution to the original full LASSO problem. Such an incremental procedure and theoretical convergence guarantee can be extended to fused LASSO problems. Compared with state-of-the-art screening methods as well as working set and homotopy methods, which may not always guarantee the optimal solution, SAIF can achieve superior or comparable efficiency and high scalability with the safe guarantee when facing extremely high dimensional data sets. Experiments with both synthetic and real-world data sets show that SAIF can be up to 50 times faster than dynamic screening, and hundreds of times faster than computing LASSO or fused LASSO solutions without screening.