Jun Yan
Multivariate Distributionally Robust Convex Regression under Absolute Error Loss
Jose Blanchet, Peter W. Glynn, Jun Yan, Zhengqing Zhou
This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein perturbations of the empirical measure) of the absolute regression errors. The inner maximization is solved in closed form resulting in a regularization penalty involves the norm of the gradient.