Post-processing for Fair Regression via Explainable SVD

Zhiqun Zuo, Ding Zhu, Mohammad Mahdi Khalili
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:1711-1719, 2025.

Abstract

This paper presents a post-processing algorithm for training fair neural network regression models that satisfy statistical parity, utilizing an explainable singular value decomposition (SVD) of the weight matrix. We propose a linear transformation of the weight matrix, whereby the singular values derived from the SVD of the transformed matrix directly correspond to the differences in the first and second moments of the output distributions across two groups. Consequently, we can convert the fairness constraints into constraints on the singular values. We analytically solve the problem of finding the optimal weights under these constraints. Experimental validation on various datasets demonstrates that our method achieves a similar or superior fairness-accuracy trade-off compared to the baselines without using the sensitive attribute at the inference time.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-zuo25a, title = {Post-processing for Fair Regression via Explainable SVD}, author = {Zuo, Zhiqun and Zhu, Ding and Khalili, Mohammad Mahdi}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {1711--1719}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/zuo25a/zuo25a.pdf}, url = {https://proceedings.mlr.press/v258/zuo25a.html}, abstract = {This paper presents a post-processing algorithm for training fair neural network regression models that satisfy statistical parity, utilizing an explainable singular value decomposition (SVD) of the weight matrix. We propose a linear transformation of the weight matrix, whereby the singular values derived from the SVD of the transformed matrix directly correspond to the differences in the first and second moments of the output distributions across two groups. Consequently, we can convert the fairness constraints into constraints on the singular values. We analytically solve the problem of finding the optimal weights under these constraints. Experimental validation on various datasets demonstrates that our method achieves a similar or superior fairness-accuracy trade-off compared to the baselines without using the sensitive attribute at the inference time.} }
Endnote
%0 Conference Paper %T Post-processing for Fair Regression via Explainable SVD %A Zhiqun Zuo %A Ding Zhu %A Mohammad Mahdi Khalili %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-zuo25a %I PMLR %P 1711--1719 %U https://proceedings.mlr.press/v258/zuo25a.html %V 258 %X This paper presents a post-processing algorithm for training fair neural network regression models that satisfy statistical parity, utilizing an explainable singular value decomposition (SVD) of the weight matrix. We propose a linear transformation of the weight matrix, whereby the singular values derived from the SVD of the transformed matrix directly correspond to the differences in the first and second moments of the output distributions across two groups. Consequently, we can convert the fairness constraints into constraints on the singular values. We analytically solve the problem of finding the optimal weights under these constraints. Experimental validation on various datasets demonstrates that our method achieves a similar or superior fairness-accuracy trade-off compared to the baselines without using the sensitive attribute at the inference time.
APA
Zuo, Z., Zhu, D. & Khalili, M.M.. (2025). Post-processing for Fair Regression via Explainable SVD. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:1711-1719 Available from https://proceedings.mlr.press/v258/zuo25a.html.

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