A0883
Title: Extremal random forests
Authors: Nicola Gnecco - University of Geneva (Switzerland) [presenting]
Edossa Merga Terefe - University of Geneva (Switzerland)
Sebastian Engelke - University of Geneva (Switzerland)
Abstract: Classical methods for quantile regression fail in cases where the quantile of interest is extreme, and only a 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. A method for extreme quantile regression that combines the flexibility of random forests with the theory of extrapolation is proposed. The extremal random forest (ERF) estimates the parameters of a generalized Pareto distribution, conditional on the predictor vector, by maximizing a local likelihood with weights extracted from a quantile random forest. The shape parameter is penalized in this likelihood to regularize its variability in the predictor space. Under the general domain of attraction conditions, we show the consistency of the estimated parameters in both the unpenalized and penalized cases. Simulation studies show that the ERF outperforms both classical quantile regression methods and existing regression approaches from extreme value theory. The methodology is applied to extreme quantile prediction for U.S. wage data.
