Adversarial Regression with Doubly Non-negative Weighting Matrices

Tam Le, Truyen Nguyen, Makoto Yamada, Jose Blanchet, Viet Anh Nguyen

Keywords: adversarial regression, kernel weighted regression, covariate perturbation, distributional robust, doubly non-negative matrices, Bures-Wasserstein, Log-determinant divergence, low-sample-size problem

TL;DR: Adversarial Regression with Doubly Non-negative Weighting Matrices

Abstract: 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.

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Code: https://github.com/lttam/Adversarial-Regression