We study to which extent additive fairness metrics (statistical parity, equal opportunity and equalized odds) can be influenced in a multi-class classification problem by memorizing a subset of the population. We give explicit expressions for the bias resulting from memorization in terms of the label and group membership distribution of the memorized dataset and the classifier bias on the unmemorized dataset. We also characterize the memorized datasets that eliminate the bias for all three metrics considered. Finally we provide upper and lower bounds on the total probability mass in the memorized dataset that is necessary for the complete elimination of these biases.

翻译：本研究探讨了在多类别分类问题中，通过记忆部分群体数据能在多大程度上影响加性公平性指标（统计奇偶性、机会均等与均衡几率）。我们推导了记忆化所导致偏差的显式表达式，该表达式由记忆数据集的标签与群体归属分布、以及未记忆数据集上的分类器偏差共同决定。同时，我们刻画了能够消除所考察三种指标偏差的记忆数据集特征。最后，我们给出了为完全消除这些偏差所需记忆数据集总概率质量的上界与下界。