When Are Learning Biases Equivalent? A Unifying Framework for Fairness, Robustness, and Distribution Shift

TL;DR

This paper introduces a unifying theoretical framework that characterizes when different bias mechanisms in machine learning, such as fairness violations and distribution shifts, produce equivalent effects on model performance, validated across multiple datasets.

Contribution

It formalizes biases as violations of conditional independence using information theory, establishing conditions for their equivalence and enabling transfer of debiasing methods across domains.

Findings

Equivalence between spurious correlation strength and sub-population imbalance ratio.

Validation of theoretical predictions across six datasets and three architectures.

Approximate 3% worst-group accuracy difference within predicted equivalence.

Abstract

Machine learning systems exhibit diverse failure modes: unfairness toward protected groups, brittleness to spurious correlations, poor performance on minority sub-populations, which are typically studied in isolation by distinct research communities. We propose a unifying theoretical framework that characterizes when different bias mechanisms produce quantitatively equivalent effects on model performance. By formalizing biases as violations of conditional independence through information-theoretic measures, we prove formal equivalence conditions relating spurious correlations, subpopulation shift, class imbalance, and fairness violations. Our theory predicts that a spurious correlation of strength $\alpha$ produces equivalent worst-group accuracy degradation as a sub-population imbalance ratio $r \approx (1+\alpha)/(1-\alpha)$ under feature overlap assumptions. Empirical validation in six datasets and three architectures confirms that predicted equivalences hold within the accuracy of the worst group 3\%, enabling the principled transfer of debiasing methods across problem domains. This work bridges the literature on fairness, robustness, and distribution shifts under a common perspective.