We propose a distributionally robust support vector machine with a fairness constraint that encourages the classifier to be fair in view of the equality of opportunity criterion. We use a type-$\infty$ Wasserstein ambiguity set centered at the empirical distribution to model distributional uncertainty and derive an exact reformulation for worst-case unfairness measure. We establish that the model is equivalent to a mixed-binary optimization problem, which can be solved by standard off-the-shelf solvers. We further prove that the expectation of the hinge loss objective function constitutes an upper bound on the misclassification probability. Finally, we numerically demonstrate that our proposed approach improves fairness with negligible loss of predictive accuracy.
翻译:我们提出一个分布强且支持性强的矢量机,其公平性限制鼓励分类员在机会均等标准下做到公平。我们使用以经验分配为中心、以分配不确定性模型为主的瓦西斯坦(Wasserstein)型型模数模糊不清,并精确地重新制定最坏情况的不公平衡量标准。我们确定该模型相当于一个混合二元优化问题,可以通过标准现成的解决方案加以解决。我们进一步证明,对临界损失客观功能的预期构成了误分类概率的上限。最后,我们从数字上表明,我们提出的方法提高了公平性,但预测准确性的损失微乎其微。