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

TL;DR

This paper proposes a kernel-based formulation of the Equalized Odds fairness criterion, providing a unified framework to quantify and balance accuracy and fairness trade-offs in supervised fair representation learning.

Contribution

It introduces $EO_k$, a novel kernel-based fairness measure that unifies independence, separation, and calibration, with theoretical guarantees and practical computation methods.

Findings

$EO_k$ satisfies fairness criteria under different conditions.

The empirical $\, ilde{EO}_k$ can be computed efficiently with performance guarantees.

The framework offers a foundation for fair algorithm design with provable guarantees.

Abstract

This paper introduces a novel kernel-based formulation of the Equalized Odds (EO) criterion, denoted as $EO_k$, 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 (prediction $\hat{Y}$ is independent of $S$), separation (also known as equalized odds; prediction $\hat{Y}$ is independent with $S$ conditioned on target attribute $Y$), and calibration ($Y$ is independent of $S$ conditioned on the prediction $\hat{Y}$). Under both unbiased ($Y$ is independent of $S$) and biased ($Y$ depends on $S$) conditions, we show that $EO_k$ 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, $\hat{EO}_k$, a kernel-based statistic that can be computed in quadratic time, with linear-time approximations also available. A concentration inequality for $\hat{EO}_k$ 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.