An Information-Theoretic Perspective on the Relationship Between Fairness and Accuracy

Our goal is to understand the so-called trade-off between fairness and accuracy. In this work, using a tool from information theory called Chernoff information, we derive fundamental limits on this relationship that explain why the accuracy on a given dataset often decreases as fairness increases. Novel to this work, we examine the problem of fair classification through the lens of a mismatched hypothesis testing problem, i.e., where we are trying to find a classifier that distinguishes between two "ideal" distributions but instead we are given two mismatched distributions that are biased. Based on this perspective, we contend that measuring accuracy with respect to the given (possibly biased) dataset is a problematic measure of performance. Instead one should also consider accuracy with respect to an ideal dataset that is unbiased. We formulate an optimization to find such ideal distributions and show that the optimization is feasible. Lastly, when the Chernoff information for one group is strictly less than another in the given dataset, we derive the information-theoretic criterion under which collection of more features can actually improve the Chernoff information and achieve fairness without compromising accuracy on the available data.