Spline regression with automatic knot selection

Abstract

Spline regression has proven to be a useful tool for nonparametric regression. The flexibility of this function family is based on basepoints defining shifts in the behavior of the function – called knots. The question of setting the adequate number of knots and their placement is usually overcome by penalizing over the spline's overall smoothness (e.g. P-splines). However, there are areas of application where finding the best knot placement is of interest. A new method is introduced for automatically selecting knots in spline regression. The approach consists in setting many initial knots and fitting the spline regression through a penalized likelihood procedure called adaptive ridge, which discards the least relevant knots. The method – called A-splines, for adaptive splines – compares favorably with other knot selection methods: it runs way faster (∼10 to ∼400 faster) than comparable methods and has close to equal predictive performance. A-splines are applied to both simulated and real datasets.