Heteroscedastic Regression Trees for Joint Modeling of Means and Variances

• Activity Number: 369
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Thomas Loughin* and Andrew Henrey
• Companies: Simon Fraser University and Simon Fraser University
• Keywords: information criteria ; AIC ; splits ; likelihood ; normal

Abstract

Standard regression trees as proposed by Breiman et al. (1984) are not robust in the presence of heteroscedasticity. They tend to split too frequently in areas of high variability, and may miss "obvious" splits in areas of low variability. We develop an alternative split-selection criterion that has the capacity to account for local variance in the regression in an unstructured manner. The criterion is based on a normal likelihood where both the mean and variance are allowed to change arbitrarily in the two child nodes. We use a specially developed information criterion to decide between the mean-only (1-parameter) and the mean+variance (2-parameter) splits across all split locations and for pruning. We show that the new approach performs better for mean estimation than does the standard mean-only split when variances are not constant.