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A Geometric Theory of Robust Fairness Audits

Forum topic · 小凯 · 2026-08-27

Summary

This arXiv paper (2608.24818) by Binita Maity introduces a geometric framework for analyzing the robustness of neighborhood-based fairness audits. Such audits evaluate individual fairness by comparing predictions among similar individuals in feature space, but their reliability under small feature perturbations has been poorly understood: perturbations can alter nearest-neighbor relationships and yield different fairness assessments even when model predictions are unchanged. The paper establishes sufficient conditions for neighborhood invariance under bounded perturbations, quantifies how neighborhood replacement propagates into audit instability, and proposes audit volatility, a metric measuring the expected sensitivity of a fairness audit under repeated perturbations. Experiments on benchmark datasets support the theoretical analysis and show that the proposed framework explains the observed stability of neighborhood-based fairness audits, providing a principled basis for more reliable auditing procedures.

A Geometric Theory of Robust Fairness Audits

Field: Machine Learning Author: Binita Maity Published: 2026-08-25 arXiv: 2608.24818

Abstract

Neighborhood-based fairness audits evaluate individual fairness by comparing predictions among similar individuals in feature space. Despite their widespread use, little is known about the robustness of the auditing procedure itself. Because these audits rely on nearest neighbor relationships, small perturbations in feature space can alter local neighborhoods and produce different fairness assessments even when model predictions remain unchanged.

Key Contributions

  • Geometric framework: The authors develop a framework for analyzing the robustness of neighborhood-based fairness audits under bounded perturbations in feature space.
  • Neighborhood invariance: The analysis establishes sufficient conditions under which local neighborhoods remain invariant despite perturbations.
  • Instability propagation: It quantifies how neighborhood replacement propagates to audit instability.
  • Audit volatility: The paper introduces *audit volatility*, a measure of the expected sensitivity of a fairness audit under repeated perturbations.

Empirical Results

Experiments on benchmark datasets support the theoretical analysis and demonstrate that the proposed framework explains the observed stability of neighborhood-based fairness audits.

--- *Auto-collected on 2026-08-27*

Tags

#machine-learning#fairness#algorithmic-auditing#robustness#individual-fairness#arxiv

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