
The core message of this paper is to develop a general framework for regression on extremes, where the goal is to build predictive functions that perform well in regions of the input space with unusually large values. Under appropriate regular variation assumptions regarding the joint distribution of the input and output variables, the authors show that an asymptotic notion of risk can be tailored to summarize predictive performance in extreme regions, and that minimization of an empirical version of this 'extreme risk' yields good generalization capacity.


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predicting-extreme-values-in-regression-problems-with-heavy-tailed-inputs


Predicting Extreme Values in Regression Problems with Heavy-Tailed Inputs


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The authors develop a projected Wasserstein distance to circumvent the curse of dimensionality in high-dimensional two-sample testing, and provide theoretical guarantees for the finite-sample convergence rate of the proposed distance.


improving-high-dimensional-two-sample-testing-via-projected-wasserstein-distance


Improving High-Dimensional Two-Sample Testing via Projected Wasserstein Distance
