×

zbMATH — the first resource for mathematics

Quantifying uncertainty in random forests via confidence intervals and hypothesis tests. (English) Zbl 1360.62095
Summary: This work develops formal statistical inference procedures for predictions generated by supervised learning ensembles. 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 data set are provided.

MSC:
62F12 Asymptotic properties of parametric estimators
60F05 Central limit and other weak theorems
62G09 Nonparametric statistical resampling methods
62H30 Classification and discrimination; cluster analysis (statistical aspects)
Software:
BayesTree
PDF BibTeX XML Cite
Full Text: Link