Tree-based boosting with functional data

TL;DR

This paper introduces a novel boosting algorithm for functional data regression using multi-index decision trees, demonstrating superior performance in simulations and real-world electricity demand prediction.

Contribution

It proposes a new boosting method with functional multi-index trees, including identifiability conditions and algorithms, advancing functional data analysis techniques.

Findings

The method performs consistently among top in simulations.

It outperforms competitors in electricity demand prediction.

Performance varies across different settings.

Abstract

In this article we propose a boosting algorithm for regression with functional explanatory variables and scalar responses. The algorithm uses decision trees constructed with multiple projections as the "base-learners", which we call "functional multi-index trees". We establish identifiability conditions for these trees and introduce two algorithms to compute them. We use numerical experiments to investigate the performance of our method and compare it with several linear and nonlinear regression estimators, including recently proposed nonparametric and semiparametric functional additive estimators. Simulation studies show that the proposed method is consistently among the top performers, whereas the performance of any competitor relative to others can vary substantially across different settings. In a real example, we apply our method to predict electricity demand using price curves and show that our estimator provides better predictions compared to its competitors, especially when one adjusts for seasonality.