报告题目：Consistency of the oblique decision tree and its boosting and random forest
报告人：詹浩然
邀请人：黄磊
报告时间：2025年03月14日上午16:00-17:00
报告地点：西南交通大学犀浦校区3教X30423
摘要：Classification and Regression Tree (CART), Random Forest (RF) and Gradient Boosting Tree (GBT) are probably the most popular set of statistical learning methods. However, their statistical consistency can only be proved under very restrictive assumptions on the underlying regression function. As an extension to standard CART, the oblique decision tree (ODT), which uses linear combinations of predictors as partitioning variables, has received much attention. ODT tends to perform numerically better than CART and requires fewer partitions. In this paper, we show that ODT is consistent for very general regression functions as long as they areL^2 integrable. Then, we prove the consistency of the ODT-based random forest (ODRF), whether fully grown or not. Finally, we propose an ensemble of GBT for regression by borrowing the technique of orthogonal matching pursuit and study its consistency under very mild conditions on the tree structure. After refining existing computer packages according to the established theory, extensive experiments on real data sets show that both our ensemble boosting trees and ODRF have noticeable overall improvements over RF and other forests.
报告人介绍：詹浩然，2023年博士毕业于新加坡国立大学，目前在新加坡国立大学统计与数据科学系做Research Fellow，科研兴趣主要是统计学习及其理论，包括神经网络、随机森林、boosting方法、大模型的统计理论。研究成果刊登于学术期刊The Annals of Statistics,Bernoulli, Computational Statistics & Data Analysis。
