Predefined demographic groups often overlook the subpopulations most impacted by model errors, leading to a growing emphasis on data-driven methods that pinpoint where models underperform. The emerging field of multi-group fairness addresses this by ensuring models perform well across a wide range of group-defining functions, rather than relying on fixed demographic categories. We demonstrate that recently introduced notions of multi-group fairness can be equivalently formulated as integral probability metrics (IPM). IPMs are the common information-theoretic tool that underlie definitions such as multiaccuracy, multicalibration, and outcome indistinguishably. For multiaccuracy, this connection leads to a simple, yet powerful procedure for achieving multiaccuracy with respect to an infinite-dimensional class of functions defined by a reproducing kernel Hilbert space (RKHS): first perform a kernel regression of a model’s errors, then subtract the resulting function from a model’s predictions. We combine these results to develop a post-processing method that improves multiaccuracy with respect to bounded-norm functions in an RKHS, enjoys provable performance guarantees, and, in binary classification benchmarks, achieves favorable multiaccuracy relative to competing methods.
@InProceedings{long_et_al:LIPIcs.FORC.2025.7, author = {Long, Carol Xuan and Alghamdi, Wael and Glynn, Alexander and Wu, Yixuan and Calmon, Flavio P.}, title = {{Kernel Multiaccuracy}}, booktitle = {6th Symposium on Foundations of Responsible Computing (FORC 2025)}, pages = {7:1--7:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-367-6}, ISSN = {1868-8969}, year = {2025}, volume = {329}, editor = {Bun, Mark}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.7}, URN = {urn:nbn:de:0030-drops-231341}, doi = {10.4230/LIPIcs.FORC.2025.7}, annote = {Keywords: algorithmic fairness, integral probability metrics, information theory} }
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