  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.
