  Many machine learning tasks that involve predicting an output response can be
solved by training a weighted regression model. Unfortunately, the predictive
power of this type of models may severely deteriorate under low sample sizes or
under covariate perturbations. Reweighting the training samples has aroused as
an effective mitigation strategy to these problems. In this paper, we propose a
novel and coherent scheme for kernel-reweighted regression by reparametrizing
the sample weights using a doubly non-negative matrix. When the weighting
matrix is confined in an uncertainty set using either the log-determinant
divergence or the Bures-Wasserstein distance, we show that the adversarially
reweighted estimate can be solved efficiently using first-order methods.
Numerical experiments show that our reweighting strategy delivers promising
results on numerous datasets.
