Adversarial Regression with Doubly Non-negative Weighting Matrices

TL;DR

This paper introduces a new kernel-reweighted regression method using doubly non-negative matrices for sample weights, improving robustness against small sample sizes and covariate perturbations, with efficient optimization and promising experimental results.

Contribution

It proposes a novel reweighting scheme with doubly non-negative matrices and efficient algorithms for adversarially reweighted regression.

Findings

Effective reweighting improves prediction robustness

Efficient first-order optimization algorithms developed

Numerical experiments show promising results

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.