Randomized learning and generalization of fair and private classifiers: From PAC-Bayes to stability and differential privacy

We address the problem of randomized learning and generalization of fair and private classifiers. From one side we want to ensure that sensitive information does not unfairly influence the outcome of a classifier. From the other side we have to learn from data while preserving the privacy of individual observations. We initially face this issue in the PAC-Bayes framework presenting an approach which trades off and bounds the risk and the fairness of the randomized (Gibbs) classifier. Our new approach is able to handle several different state-of-the-art fairness measures. For this purpose, we further develop the idea that the PAC-Bayes prior can be defined based on the data-generating distribution without actually knowing it. In particular, we define a prior and a posterior which give more weight to functions with good generalization and fairness properties. Furthermore, we will show that this randomized classifier …