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Kernel Multiaccuracy

Authors Carol Xuan Long , Wael Alghamdi , Alexander Glynn, Yixuan Wu, Flavio P. Calmon

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  • Mathematics of computing → Information theory
Keywords
  • algorithmic fairness
  • integral probability metrics
  • information theory

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Abstract

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.

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Carol Xuan Long, Wael Alghamdi, Alexander Glynn, Yixuan Wu, and Flavio P. Calmon. Kernel Multiaccuracy. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 7:1-7:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.FORC.2025.7

Author Details

Carol Xuan Long
  • John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
Wael Alghamdi
  • John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
Alexander Glynn
  • John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
Yixuan Wu
  • John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
Flavio P. Calmon
  • John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant No FAI 2040880, CIF 2231707, and CIF 2312667.

Supplementary Materials

References

  1. Alekh Agarwal, Alina Beygelzimer, Miroslav Dudík, John Langford, and Hanna Wallach. A reductions approach to fair classification. In International conference on machine learning, pages 60-69. PMLR, 2018. URL: http://proceedings.mlr.press/v80/agarwal18a.html.
  2. Wael Alghamdi, Hsiang Hsu, Haewon Jeong, Hao Wang, Peter Michalak, Shahab Asoodeh, and Flavio Calmon. Beyond adult and compas: Fair multi-class prediction via information projection. Advances in Neural Information Processing Systems, 35:38747-38760, 2022. Google Scholar
  3. Solon Barocas, Moritz Hardt, and Arvind Narayanan. Fairness and machine learning: Limitations and opportunities. MIT Press, 2023. Google Scholar
  4. Alain Berlinet and Christine Thomas-Agnan. Reproducing Kernel Hilbert Spaces in Probability and Statistics. Springer, 1 edition, 2004. URL: https://doi.org/10.1007/9781441990969.
  5. Stephen P Boyd and Lieven Vandenberghe. Convex optimization. Cambridge university press, 2004. Google Scholar
  6. Peng Cui, Wenbo Hu, and Jun Zhu. Calibrated reliable regression using maximum mean discrepancy. In H. Larochelle, M. Ranzato, R. Hadsell, M.F. Balcan, and H. Lin, editors, Advances in Neural Information Processing Systems, volume 33, pages 17164-17175. Curran Associates, Inc., 2020. URL: https://proceedings.neurips.cc/paper_files/paper/2020/file/c74c4bf0dad9cbae3d80faa054b7d8ca-Paper.pdf.
  7. A Philip Dawid. The well-calibrated bayesian. Journal of the American Statistical Association, 77(379):605-610, 1982. Google Scholar
  8. Zhun Deng, Cynthia Dwork, and Linjun Zhang. Happymap: A generalized multi-calibration method. arXiv preprint arXiv:2303.04379, 2023. URL: https://doi.org/10.48550/arXiv.2303.04379.
  9. Cynthia Dwork, Michael P Kim, Omer Reingold, Guy N Rothblum, and Gal Yona. Outcome indistinguishability. In Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing, pages 1095-1108, 2021. URL: https://doi.org/10.1145/3406325.3451064.
  10. Cynthia Dwork, Daniel Lee, Huijia Lin, and Pranay Tankala. From pseudorandomness to multi-group fairness and back. In The Thirty Sixth Annual Conference on Learning Theory, pages 3566-3614. PMLR, 2023. URL: https://proceedings.mlr.press/v195/dwork23a.html.
  11. Vitaly Feldman. Distribution-specific agnostic boosting. In International Conference on Supercomputing, 2009. URL: https://api.semanticscholar.org/CorpusID:2787595.
  12. Sorelle A Friedler, Carlos Scheidegger, Suresh Venkatasubramanian, Sonam Choudhary, Evan P Hamilton, and Derek Roth. A comparative study of fairness-enhancing interventions in machine learning. In Proceedings of the conference on fairness, accountability, and transparency, pages 329-338, 2019. URL: https://doi.org/10.1145/3287560.3287589.
  13. Sumegha Garg, Christopher Jung, Omer Reingold, and Aaron Roth. Oracle efficient online multicalibration and omniprediction. In Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 2725-2792. SIAM, 2024. URL: https://doi.org/10.1137/1.9781611977912.98.
  14. Ira Globus-Harris, Varun Gupta, Christopher Jung, Michael Kearns, Jamie Morgenstern, and Aaron Roth. Multicalibrated regression for downstream fairness. arXiv preprint arXiv:2209.07312, 2022. URL: https://doi.org/10.48550/arXiv.2209.07312.
  15. Ira Globus-Harris, Declan Harrison, Michael Kearns, Aaron Roth, and Jessica Sorrell. Multicalibration as boosting for regression. arXiv preprint arXiv:2301.13767, 2023. URL: https://doi.org/10.48550/arXiv.2301.13767.
  16. Robert Kent Goodrich. A riesz representation theorem. In Proc. Amer. Math. Soc, volume 24, pages 629-636, 1970. Google Scholar
  17. Parikshit Gopalan, Lunjia Hu, Michael P Kim, Omer Reingold, and Udi Wieder. Loss minimization through the lens of outcome indistinguishability. arXiv preprint arXiv:2210.08649, 2022. URL: https://doi.org/10.48550/arXiv.2210.08649.
  18. Parikshit Gopalan, Adam Tauman Kalai, Omer Reingold, Vatsal Sharan, and Udi Wieder. Omnipredictors. arXiv preprint arXiv:2109.05389, 2021. URL: https://arxiv.org/abs/2109.05389.
  19. Arthur Gretton, Karsten Borgwardt, Malte Rasch, Bernhard Schölkopf, and Alex Smola. A kernel method for the two-sample-problem. Advances in neural information processing systems, 19, 2006. Google Scholar
  20. Nika Haghtalab, Michael Jordan, and Eric Zhao. A unifying perspective on multi-calibration: Game dynamics for multi-objective learning. Advances in Neural Information Processing Systems, 36, 2024. Google Scholar
  21. Moritz Hardt, Eric Price, and Nati Srebro. Equality of opportunity in supervised learning. Advances in neural information processing systems, 29, 2016. Google Scholar
  22. Ursula Hébert-Johnson, Michael Kim, Omer Reingold, and Guy Rothblum. Multicalibration: Calibration for the (computationally-identifiable) masses. In International Conference on Machine Learning, pages 1939-1948. PMLR, 2018. Google Scholar
  23. Emmie Hine and Luciano Floridi. The blueprint for an ai bill of rights: in search of enaction, at risk of inaction. Minds and Machines, pages 1-8, 2023. Google Scholar
  24. Max Hort, Zhenpeng Chen, Jie M Zhang, Federica Sarro, and Mark Harman. Bia mitigation for machine learning classifiers: A comprehensive survey. arXiv preprint arXiv:2207.07068, 2022. URL: https://doi.org/10.48550/arXiv.2207.07068.
  25. Faisal Kamiran, Asim Karim, and Xiangliang Zhang. Decision theory for discrimination-aware classification. In 2012 IEEE 12th international conference on data mining, pages 924-929. IEEE, 2012. URL: https://doi.org/10.1109/ICDM.2012.45.
  26. Michael Kearns, Seth Neel, Aaron Roth, and Zhiwei Steven Wu. Preventing fairness gerrymandering: Auditing and learning for subgroup fairness. In International conference on machine learning, pages 2564-2572. PMLR, 2018. Google Scholar
  27. Been Kim, Rajiv Khanna, and Oluwasanmi O Koyejo. Examples are not enough, learn to criticize! criticism for interpretability. Advances in neural information processing systems, 29, 2016. Google Scholar
  28. Michael P Kim, Amirata Ghorbani, and James Zou. Multiaccuracy: Black-box post-processing for fairness in classification. In Proceedings of the 2019 AAAI/ACM Conference on AI, Ethics, and Society, pages 247-254, 2019. URL: https://doi.org/10.1145/3306618.3314287.
  29. Michael P. Kim, Christoph Kern, Shafi Goldwasser, and Frauke Krueter. Universal adaptability: Target-independent inference that competes with propensity scoring. Proceedings of the National Academy of Sciences, page 119(4):e2108097119, 2022. Google Scholar
  30. Aviral Kumar, Sunita Sarawagi, and Ujjwal Jain. Trainable calibration measures for neural networks from kernel mean embeddings. In International Conference on Machine Learning, pages 2805-2814. PMLR, 2018. Google Scholar
  31. Carol Xuan Long, Hsiang Hsu, Wael Alghamdi, and Flavio Calmon. Individual arbitrariness and group fairness. In Thirty-seventh Conference on Neural Information Processing Systems, 2023. Google Scholar
  32. Charles Marx, Sofian Zalouk, and Stefano Ermon. Calibration by distribution matching: Trainable kernel calibration metrics. arXiv preprint arXiv:2310.20211, 2023. URL: https://doi.org/10.48550/arXiv.2310.20211.
  33. Alfred Müller. Integral probability metrics and their generating classes of functions. Advances in applied probability, 29(2):429-443, 1997. Google Scholar
  34. Alexandru Niculescu-Mizil and Rich Caruana. Predicting good probabilities with supervised learning. In Proceedings of the 22nd international conference on Machine learning, pages 625-632, 2005. URL: https://doi.org/10.1145/1102351.1102430.
  35. F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay. Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12:2825-2830, 2011. URL: https://doi.org/10.5555/1953048.2078195.
  36. Hao Song, Tom Diethe, Meelis Kull, and Peter Flach. Distribution calibration for regression. In International Conference on Machine Learning, pages 5897-5906. PMLR, 2019. URL: http://proceedings.mlr.press/v97/song19a.html.
  37. Bharath K Sriperumbudur, Kenji Fukumizu, Arthur Gretton, Bernhard Schölkopf, and Gert RG Lanckriet. On the empirical estimation of integral probability metrics, 2012. Google Scholar
  38. Bharath K Sriperumbudur, Kenji Fukumizu, and Gert RG Lanckriet. Universality, characteristic kernels and rkhs embedding of measures. Journal of Machine Learning Research, 12(7), 2011. Google Scholar
  39. David Widmann, Fredrik Lindsten, and Dave Zachariah. Calibration tests in multi-class classification: A unifying framework. Advances in neural information processing systems, 32, 2019. Google Scholar
  40. David Widmann, Fredrik Lindsten, and Dave Zachariah. Calibration tests beyond classification. arXiv preprint arXiv:2210.13355, 2022. URL: https://doi.org/10.48550/arXiv.2210.13355.
  41. Lujing Zhang, Aaron Roth, and Linjun Zhang. Fair risk control: A generalized framework for calibrating multi-group fairness risks. arXiv preprint arXiv:2405.02225, 2024. URL: https://doi.org/10.48550/arXiv.2405.02225.
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