Section 1 describes the set-up of the problem. In particular, the authors emphasize that there are two cases where features might have noise in them: 1) when noise is deliberately added by researchers for privacy purposes and 2) in the "positive and unlabeled" setting where individual participants in the minority group might feel uncomfortable disclosing that, leading to unlabeled data for the sensitive feature in some cases. The case under consideration is binary classification on output Y with a binary sensitive feature A . There are two main assumptions in this paper. The first is that the noise can be described as "mutually contaminated learning".

Fair classification has been a topic of intense study in machine learning, and several algorithms have been proposed towards this important task. However, in a recent study, Friedler et al. observed that fair classification algorithms may not be stable with respect to variations in the training dataset -- a crucial consideration in several real-world applications. Motivated by their work, we study the problem of designing classification algorithms that are both fair and stable. We propose an extended framework based on fair classification algorithms that are formulated as optimization problems, by introducing a stability-focused regularization term. Theoretically, we prove a stability guarantee, that was lacking in fair classification algorithms, and also provide an accuracy guarantee for our extended framework. Our accuracy guarantee can be used to inform the selection of the regularization parameter in our framework. To the best of our knowledge, this is the first work that combines stability and fairness in automated decision-making tasks. We assess the benefits of our approach empirically by extending several fair classification algorithms that are shown to achieve the best balance between fairness and accuracy over the Adult dataset. Our empirical results show that our framework indeed improves the stability at only a slight sacrifice in accuracy.