Fair Risk Control: A Generalized Framework for Calibrating Multi-group Fairness Risks

A common theme across the fairness in machine learning literature is that some measure of error or risk should be equalized across sub-populations. Common measures evaluated across demographic groups include false positive and false negative rates (Hardt et al., 2016) and calibration error (Kleinberg et al., 2016; Chouldechova, 2017). Initial work in this line gave methods for equalizing different risk measures on disjoint groups. A second generation of work gave methods for equalizing measures of risk across groups even when the groups could intersect - e.g. for false positive and negative rates (Kearns et al., 2018), calibration error (Úrsula Hébert-Johnson et al., 2018), regret (Blum & Lykouris, 2019; Rothblum & Yona, 2021), prediction set coverage (Jung et al., 2021, 2022; Deng et al., 2023), among other risk measures. In general, distinct algorithms are derived for each of these settings, and they are generally limited to one-dimensional predictors of various sorts. In this work, we propose a unifying framework for fair risk control in settings with multi-dimensional outputs, based on multicalibration (Úrsula Hébert-Johnson et al., 2018). This framework is developed as an extension of the work by Deng et al. (2023); Noarov & Roth (2023), and addresses the need for calibrating multi-dimensional output functions. To illustrate the usefulness of this framework, we apply it to a variety of settings, including false negative rate control in image segmentation, prediction set conditional coverage guarantees in hierarchical classification, and de-biased text generation in language models. These applications make use of the additional power granted by our multi-dimensional extension of multicalibration.