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Activity Number: 343
Type: Contributed
Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Mining
Abstract #311320 View Presentation
Title: The Effect of Heteroscedasticity on Regression Trees
Author(s): Thomas Loughin*+ and William Ruth
Companies: Simon Fraser University and Simon Fraser University
Keywords: squared error loss ; splits ; prediction ; recursive partitioning ; simulation
Abstract:

Regression trees are becoming increasingly popular as omnibus predicting tools. They also form the basis of numerous modern statistical learning ensembles, like random forests and Bayesian adaptive regression trees. Part of their popularity is their ability to create a regression prediction without ever specifying a structure for the mean model. However, it is not often mentioned that the method does implicitly assume homogeneous variance across the entire explanatory-variable space. It is unknown how the algorithm behaves when faced with heteroscedastic data. In this study, we assess the performance of the most popular regression-tree algorithm in a single-variable setting under a very simple step-function model for heteroscedasticity. We use simulation to show that the locations of splits and hence the ability to accurately predict means are both are influenced by the change in variance.


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