Efficient Tuning of Elastic Net Based on Subdivision For Bezier Simplex Fitting

Abstract

Elastic net, a popular sparse modeling technique, has 2 hyperparameters and, hence, studies on tuning have been conducted. Although the solution map can be approximated with a geometrical shape called Bezier simplex, this requires a high-order polynomial regression, resulting in a complex computation. We thus propose to lower the order by subdividing the Bezier simplex into smaller ones. The subdivision is recursive. Following existing work, we evaluated the method by using qsar-fish-toxicity data. It was implied that the subdivision indeed achieves the same accuracy with a lower order and that parallel computation would reduce the training cost.