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Activity Number: 377
Type: Contributed
Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Mining
Abstract - #309998
Title: Inference for Supervised Learning: Regression Trees and CLTs
Author(s): Lucas Mentch*+ and Giles Hooker
Companies: Cornell University and Cornell University
Keywords: Tree ; CART ; Machine Learning ; U-Statistics
Abstract:

This presentation introduces initial steps towards inference using ensemble-tree methods. Ensemble methods based on bootstrapping have improved the predictive accuracy of individual trees, but fail to provide a framework in which distributional results can be easily determined. Instead of aggregating bootstrap samples, we consider predicting by averaging over trees built on subsamples of the training set and demonstrate that such an estimator takes a form similar to that of a U-statistic. As such, predictions for individual feature vectors are asymptotically normal, thereby allowing for confidence intervals to accompany predictions. We derive rates at which the subsample size may grow with total sample size to establish these results. Frequently, a subset of subsamples will be used for computational speed; here our estimators take a form similar to incomplete U-statistics and equivalent results can be derived. We end by demonstrating that this setup also provides a framework for testing significance of individual features.


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