This paper introduces a framework for post-processing machine learning models so that their predictions satisfy multi-group fairness guarantees. Based on the celebrated notion of multicalibration, we introduce $(\mathbf{s},\mathcal{G}, \alpha)-$GMC (Generalized Multi-Dimensional Multicalibration) for multi-dimensional mappings $\mathbf{s}$, constraint set $\mathcal{G}$, and a pre-specified threshold level $\alpha$. We propose associated algorithms to achieve this notion in general settings. This framework is then applied to diverse scenarios encompassing different fairness concerns, including false negative rate control in image segmentation, prediction set conditional uncertainty quantification in hierarchical classification, and de-biased text generation in language models. We conduct numerical studies on several datasets and tasks.

翻译：本文提出了一种机器学习模型后处理框架，使其预测满足多组公平性保障。基于著名的多重校准概念，我们针对多维映射$\mathbf{s}$、约束集$\mathcal{G}$和预设阈值$\alpha$引入了$(\mathbf{s},\mathcal{G}, \alpha)-$GMC（广义多维多重校准）。我们提出了在一般设置下实现该概念的相应算法。该框架随后被应用于涵盖不同公平性关注点的多种场景，包括图像分割中的假阴性率控制、层次分类中预测集合的条件不确定性量化，以及语言模型中的去偏文本生成。我们在多个数据集和任务上进行了数值研究。