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

Yijin Ni, Xiaoming Huo

Keywords: Fair Representation Learning, Kernel Methods, Equalized Odds, Demographic Parity, Fairness-Accuracy Trade-off

TL;DR: We propose a kernel-based equalized statistic to quantify the accuracy-fairness trade-off among independence-, separation-, and calibration-based constraints, identifying the best suited criterion to preserve predictive accuracy.

Abstract:

This paper introduces a novel kernel-based formulation of the Equalized Odds (EO) criterion, denoted as $\operatorname{EO}_k$, 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 ($\widehat{Y} \perp S$),
separation—also known as equalized odds ($\widehat{Y} \perp S \mid Y$), and calibration ($Y \perp S \mid \widehat{Y}$).
Under both unbiased ($Y \perp S$) and biased ($Y \not \perp S$) conditions, we show that $\operatorname{EO}_k$ 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, $\widehat{\operatorname{EO}}_k$, a kernel-based statistic that can be computed in quadratic time, with linear-time approximations also available.
A concentration inequality for $\widehat{\operatorname{EO}}_k$ 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.

Primary Area: Theory (e.g., control theory, learning theory, algorithmic game theory)

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Submission Number: 22476