Ridge regression with adaptive additive rectangles and other piecewise functional templates

71/2020

Ridge regression with adaptive additive rectangles and other piecewise functional templates

Saturday 7th November 2020

Belli E; Vantini S.

We propose an L2-based penalization algorithm for functional linear regression models, where the coefficient function is shrunk towards a data-driven shape template ?, which is constrained to belong to a class of piecewise functions by restricting its basis expansion. In particular, we focus on the case where ? can be expressed as a sum of q rectangles that are adaptively positioned with respect to the regression error. As the problem of finding the optimal knot placement of a piecewise function is nonconvex, the proposed parametrization allows to reduce the number of variables in the global optimization scheme, resulting in a fitting algorithm that alternates between approximating a suitable template and solving a convex ridge-like problem. The predictive power and interpretability of our method is shown on multiple simulations and two real world case studies.