Segmented Linear Regression Trees  

作　　者：Xiangyu Zheng Songxi Chen 

机构地区：[1]JD Technology,Beijing 100176,P.R.China [2]Department of Statistics and Data Science,Tsinghua University,Beijing 100084,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2025年第2期498-521,共24页数学学报(英文版)

摘　　要：Tree-based models have been widely applied in both academic and industrial settings due to the natural interpretability, good predictive accuracy, and high scalability. In this paper, we focus on improving the single-tree method and propose the segmented linear regression trees(SLRT) model that replaces the traditional constant leaf model with linear ones. From the parametric view, SLRT can be employed as a recursive change point detect procedure for segmented linear regression(SLR) models,which is much more efficient and flexible than the traditional grid search method. Along this way,we propose to use the conditional Kendall's τ correlation coefficient to select the underlying change points. From the non-parametric view, we propose an efficient greedy splitting method that selects the splits by analyzing the association between residuals and each candidate split variable. Further, with the SLRT as a single-tree predictor, we propose a linear random forest approach that aggregates the SLRTs by a weighted average. Both simulation and empirical studies showed significant improvements than the CART trees and even the random forest.

关 键 词：Regression trees segmented linear regression split selection tree pruning 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]