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Title: Extremal random forests Authors:  Sebastian Engelke - University of Geneva (Switzerland) [presenting]
Nicola Gnecco - University of Geneva (Switzerland)
Edossa Merga Terefe - University of Geneva (Switzerland)
Abstract: Quantile regression relies on minimizing the conditional quantile loss. This has been extended to flexible regression functions such as the gradient forest. These methods break down if the quantile of interest lies outside of the range of the data. Extreme value theory provides the mathematical foundation for the estimation of such extreme quantiles. A common approach is to approximate the exceedances over a high threshold by the generalized Pareto distribution. For conditional extreme quantiles, one may model this distribution's parameters as the predictors' functions. Up to now, the existing methods are either not flexible enough or do not generalize well in higher dimensions. We develop a new approach for extreme quantile regression based on random forests that estimates the parameters of the generalized Pareto distribution flexibly, even in higher dimensions. This estimator outperforms classical quantile regression methods and methods from extreme value theory in simulation studies. We illustrate the methodology with the example of U.S. wage data.