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On the Impact of Multi-dimensional Local Differential Privacy on Fairness

Karima Makhlouf, Heber H. Arcolezi, Sami Zhioua, Ghassen Ben Brahim, Catuscia Palamidessi

TL;DR

The paper investigates how local differential privacy via $k$-ary Randomized Response affects fairness when multiple sensitive attributes are obfuscated. It compares independent and combined perturbation strategies for multi-dimensional data and analyzes how the outcome distribution $Y$ shapes the privacy-fairness-utility trade-off. Key findings show that multi-dimensional LDP generally reduces disparity, with combined perturbation offering efficiency at weaker privacy guarantees, and that the distribution of the outcome critically influences which group is most impacted. The work provides concrete recommendations for practitioners to balance privacy, fairness, and utility in ML applications and points to future work on formalizing the trade-offs and developing fairness-aware LDP methods.

Abstract

Automated decision systems are increasingly used to make consequential decisions in people's lives. Due to the sensitivity of the manipulated data as well as the resulting decisions, several ethical concerns need to be addressed for the appropriate use of such technologies, in particular, fairness and privacy. Unlike previous work, which focused on centralized differential privacy (DP) or local DP (LDP) for a single sensitive attribute, in this paper, we examine the impact of LDP in the presence of several sensitive attributes (i.e., multi-dimensional data) on fairness. Detailed empirical analysis on synthetic and benchmark datasets revealed very relevant observations. In particular, (1) multi-dimensional LDP is an efficient approach to reduce disparity, (2) the multi-dimensional approach of LDP (independent vs. combined) matters only at low privacy guarantees, and (3) the outcome Y distribution has an important effect on which group is more sensitive to the obfuscation. Last, we summarize our findings in the form of recommendations to guide practitioners in adopting effective privacy-preserving practices while maintaining fairness and utility in ML applications.

On the Impact of Multi-dimensional Local Differential Privacy on Fairness

TL;DR

The paper investigates how local differential privacy via -ary Randomized Response affects fairness when multiple sensitive attributes are obfuscated. It compares independent and combined perturbation strategies for multi-dimensional data and analyzes how the outcome distribution shapes the privacy-fairness-utility trade-off. Key findings show that multi-dimensional LDP generally reduces disparity, with combined perturbation offering efficiency at weaker privacy guarantees, and that the distribution of the outcome critically influences which group is most impacted. The work provides concrete recommendations for practitioners to balance privacy, fairness, and utility in ML applications and points to future work on formalizing the trade-offs and developing fairness-aware LDP methods.

Abstract

Automated decision systems are increasingly used to make consequential decisions in people's lives. Due to the sensitivity of the manipulated data as well as the resulting decisions, several ethical concerns need to be addressed for the appropriate use of such technologies, in particular, fairness and privacy. Unlike previous work, which focused on centralized differential privacy (DP) or local DP (LDP) for a single sensitive attribute, in this paper, we examine the impact of LDP in the presence of several sensitive attributes (i.e., multi-dimensional data) on fairness. Detailed empirical analysis on synthetic and benchmark datasets revealed very relevant observations. In particular, (1) multi-dimensional LDP is an efficient approach to reduce disparity, (2) the multi-dimensional approach of LDP (independent vs. combined) matters only at low privacy guarantees, and (3) the outcome Y distribution has an important effect on which group is more sensitive to the obfuscation. Last, we summarize our findings in the form of recommendations to guide practitioners in adopting effective privacy-preserving practices while maintaining fairness and utility in ML applications.
Paper Structure (20 sections, 3 equations, 6 figures, 2 tables)

This paper contains 20 sections, 3 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries and Notation
  4. Problem Statement
  5. Local Differential Privacy
  6. Fairness
  7. Combined vs independent $k$-RR
  8. Empirical Results and Analysis
  9. Impact of LDP on fairness
  10. $k$-RR-Ind vs $k$-RR-Comb
  11. The effect of changing the outcome distribution
  12. Recommendations
  13. A. LDP data obfuscation is an efficient mechanism to reduce disparity.
  14. B. Obfuscating several sensitive attributes allows to reduce disparity more efficiently than a single attribute.
  15. C. Independent and combined variants of multi-dimensional LDP are different only with weak privacy guarantees.
  16. ...and 5 more sections

Figures (6)

  • Figure 1: Our framework for fairness assessment when learning over LDP-based data.
  • Figure 2: Causal Model of the Synthetic Dataset.
  • Figure 5: Impact of Y distribution on the privacy-fairness trade-off. Columns 1, 2, and 3 illustrate the results for the Adult dataset when the Y distribution is skewed to 1, balanced, and skewed to 0, respectively.
  • Figure 6: Impact of $k$-RR on fairness for the Adult datasets generated with three different thresholds leading to different Y distributions. Synthetic data 2
  • Figure 7: Impact of Y distribution on the privacy-fairness trade-off. Columns 1, 2, and 3 illustrate the results for the synthetic dataset when the Y distribution is skewed to 1, balanced, and skewed to 0, respectively.
  • ...and 1 more figures

Theorems & Definitions (2)

  • Definition 1: $\epsilon$-Local Differential Privacy
  • Definition 2