Enhancing safe screening rules with adaptive thresholding for non-overlapping group sparse norm regularized problems

Sparsity is an often desired property in machine learning and signal processing problems. Recently, techniques such as screening rules were proposed to exploit sparsity in order to diminish the computational requirements of large and huge-scale optimization problems. Nevertheless, existing methods provide rough estimations of the solution support discarding only a few entries in the solution, thus limiting the desired computational savings. In this paper, we propose a simple and computationally cheap modification for safe screening rules based on automatic thresholding and the observation that the screening metric has a distribution that, for practical purposes, can be considered unimodal. The proposed method is evaluated for MEG / EEG source imaging and image classification. Computational results indicate that the proposed screening scheme outperforms the safe method costing only minor losses in accuracy and yields approximate speedups of up to 167.59 for MEG / EEG source imaging, and up to 2.12 for image classification.