Tree-Values: selective inference for regression trees

• URL: http://arxiv.org/abs/2106.07816v1
• Date: Tue, 15 Jun 2021 00:25:11 GMT
• Title: Tree-Values: selective inference for regression trees
• Authors: Anna C. Neufeld, Lucy L. Gao, Daniela M. Witten
• Abstract summary: A naive approach to inference that does not account for the fact that the tree was estimated from the data will not achieve standard guarantees. We propose a selective inference framework for conducting inference on a fitted CART tree.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider conducting inference on the output of the Classification and Regression Tree (CART) [Breiman et al., 1984] algorithm. A naive approach to inference that does not account for the fact that the tree was estimated from the data will not achieve standard guarantees, such as Type 1 error rate control and nominal coverage. Thus, we propose a selective inference framework for conducting inference on a fitted CART tree. In a nutshell, we condition on the fact that the tree was estimated from the data. We propose a test for the difference in the mean response between a pair of terminal nodes that controls the selective Type 1 error rate, and a confidence interval for the mean response within a single terminal node that attains the nominal selective coverage. Efficient algorithms for computing the necessary conditioning sets are provided. We apply these methods in simulation and to a dataset involving the association between portion control interventions and caloric intake.

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