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. One finds optimal projections over the entire tree, while the other one searches for a single optimal projection at each split.
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.
Xiaomeng Ju
PhD candidate in Statistics
I am a PhD student in Statistics at the University of British Columbia, advised by Professor Matias Salibian-Barrera. She received her BSc in Statistics from Renmin University of China, and MA in Statistics from University of Michigan. Xiaomeng’s research is centred on computational statistics with a special focus on robust statistics and functional data. Her ongoing thesis work develops gradient boosting methods for regression problems with complex data.