Extremal Random Forests

Understand

Classical methods for quantile regression fail in cases where the quantile of interest is extreme and only few or no training data points exceed it.

• Asymptotic results from extreme value theory can be used to extrapolate beyond the range of the data, and several approaches exist that use linear regression, kernel methods or generalized additive models.
• Most of these methods break down if the predictor space has more than a few dimensions or if the regression function of extreme quantiles is complex.
• We propose a method for extreme quantile regression that combines the flexibility of random forests with the theory of extrapolation.