Ensemble Trees and CLTs: Statistical Inference for Supervised Learning
Year: 2014
Type: preprint
Abstract: This work develops formal statistical inference procedures for machine learning ensemble methods. Ensemble methods based on bootstrapping, such as bagging and random forests, 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 full bootstrap samples, we consider predicting by averaging over trees built on subsamples of the training set and demonstrate that the resulting estimator takes the form of a U-statistic. As such, predictions for individual feature vectors are asymptotically normal, allowing for confidence intervals to accompany predictions. In practice, a subset of subsamples is used for computational speed; here our estimators take the form of incomplete U-statistics and equivalent results are derived. We further demonstrate that this setup provides a framework for testing the significance of features. Moreover, the internal estimation method we develop allows us to estimate the variance parameters and perform these inference procedures at no additional computational cost. Simulations and illustrations on a real dataset are provided.
Source: arXiv (Cornell University)
Authors: Lucas Mentch, Giles Hooker
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2749416011