Uncertainty quantification for honest regression trees

Abstract A new method is developed for quantifying the uncertainties of the estimates and predictions produced by honest random forests. This new method is based on the generalized fiducial methodology, and provides a fiducial density function that measures how likely each single honest tree is the true model. With such a density function, estimates and predictions, as well as their confidence/prediction intervals, can be obtained. The promising empirical properties of the proposed method are demonstrated by numerical comparisons with several state-of-the-art methods, and by applications to a few real data sets. Lastly, the proposed method is theoretically backed up by an asymptotic guarantee.