# Kernel-based Equalized Odds: A Quantification of Accuracy-Fairness Trade-off in Fair Representation Learning

arXiv: https://arxiv.org/abs/2508.15084 · HTML: https://mlsanity.com/paper/2508.15084/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 29 references that are in the map.
- First posted on arXiv 20 Aug 2025.

## Builds on (most cited first, 14 of 14)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Learning Adversarially Fair and Transferable Representations](https://mlsanity.com/paper/1802.06309/) (2018)
- [Data Decisions and Theoretical Implications when Adversarially Learning Fair Representations](https://mlsanity.com/paper/1707.00075/) (2017)
- [Conditional Learning of Fair Representations](https://mlsanity.com/paper/1910.07162/) (2019)
- [Statistical Inference for Generative Models with Maximum Mean Discrepancy](https://mlsanity.com/paper/1906.05944/) (2019)
- [Characteristic and Universal Tensor Product Kernels](https://mlsanity.com/paper/1708.08157/) (2017)
- [Learning fair representation with a parametric integral probability metric](https://mlsanity.com/paper/2202.02943/) (2022)
- [Fair Representation: Guaranteeing Approximate Multiple Group Fairness for Unknown Tasks](https://mlsanity.com/paper/2109.00545/) (2021)
- [MMD-B-Fair: Learning Fair Representations with Statistical Testing](https://mlsanity.com/paper/2211.07907/) (2022)
- [Boosting the Power of Kernel Two-Sample Tests](https://mlsanity.com/paper/2302.10687/) (2023)
- [Fair Representation Learning for Continuous Sensitive Attributes using Expectation of Integral Probability Metrics](https://mlsanity.com/paper/2505.06435/) (2025)
- [Metrizing Fairness](https://mlsanity.com/paper/2205.15049/) (2022)
- [10 Years of Fair Representations: Challenges and Opportunities](https://mlsanity.com/paper/2407.03834/) (2024)

## Abstract (arXiv)

This paper introduces a novel kernel-based formulation of the Equalized Odds (EO) criterion, denoted as EOk, for fair representation learning (FRL) in supervised settings. The central goal of FRL is to mitigate discrimination regarding a sensitive attribute S while preserving prediction accuracy for the target variable Y. Our proposed criterion enables a rigorous and interpretable quantification of three core fairness objectives: independence (prediction hatY is independent of S), separation (also known as equalized odds; prediction hatY is independent with S conditioned on target attribute Y), and calibration (Y is independent of S conditioned on the prediction hatY). Under both unbiased (Y is independent of S) and biased (Y depends on S) conditions, we show that EOk satisfies both independence and separation in the former, and uniquely preserves predictive accuracy while lower bounding independence and calibration in the latter, thereby offering a unified analytical characterization of the tradeoffs among these fairness criteria. We further define the empirical counterpart, hatEOk, a kernel-based statistic that can be computed in quadratic time, with linear-time approximations also available. A concentration inequality for hatEOk is derived, providing performance guarantees and error bounds, which serve as practical certificates of fairness compliance. While our focus is on theoretical development, the results lay essential groundwork for principled and provably fair algorithmic design in future empirical studies.