Prediction regions for functional-valued random forests

Abstract

We propose prediction regions for Random Forests (RFs) with functional output. Our approach is based on a metric specification and builds on the notion of Fréchet regression. It leverages the Out-Of-Bag (OOB) observations naturally generated during the training of RFs to estimate the uncertainty in the prediction, using the complete dataset. We outline the assumptions underpinning the construction of the prediction regions through OOB errors. A numerical experiment with quantile curves on the response and scalar predictor illustrates the prediction regions and shows that four types of nominal coverages are honored.