Ridge regression with adaptive additive rectangles and other piecewise functional templates

• URL: http://arxiv.org/abs/2011.01048v1
• Date: Mon, 2 Nov 2020 15:28:54 GMT
• Title: Ridge regression with adaptive additive rectangles and other piecewise functional templates
• Authors: Edoardo Belli, Simone Vantini
• Abstract summary: We propose an $L_2$-based penalization algorithm for functional linear regression models. We show how our algorithm alternates between approximating a suitable template and solving a convex ridge-like problem.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose an $L_{2}$-based penalization algorithm for functional linear regression models, where the coefficient function is shrunk towards a data-driven shape template $\gamma$, which is constrained to belong to a class of piecewise functions by restricting its basis expansion. In particular, we focus on the case where $\gamma$ 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.

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