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FairRR: Pre-Processing for Group Fairness through Randomized Response

Xianli Zeng, Joshua Ward, Guang Cheng

TL;DR

It is shown that measures of group fairness can be directly controlled for with optimal model utility, and proposed a pre-processing algorithm called FairRR that yields excellent downstream model utility and fairness.

Abstract

The increasing usage of machine learning models in consequential decision-making processes has spurred research into the fairness of these systems. While significant work has been done to study group fairness in the in-processing and post-processing setting, there has been little that theoretically connects these results to the pre-processing domain. This paper proposes that achieving group fairness in downstream models can be formulated as finding the optimal design matrix in which to modify a response variable in a Randomized Response framework. We show that measures of group fairness can be directly controlled for with optimal model utility, proposing a pre-processing algorithm called FairRR that yields excellent downstream model utility and fairness.

FairRR: Pre-Processing for Group Fairness through Randomized Response

TL;DR

It is shown that measures of group fairness can be directly controlled for with optimal model utility, and proposed a pre-processing algorithm called FairRR that yields excellent downstream model utility and fairness.

Abstract

The increasing usage of machine learning models in consequential decision-making processes has spurred research into the fairness of these systems. While significant work has been done to study group fairness in the in-processing and post-processing setting, there has been little that theoretically connects these results to the pre-processing domain. This paper proposes that achieving group fairness in downstream models can be formulated as finding the optimal design matrix in which to modify a response variable in a Randomized Response framework. We show that measures of group fairness can be directly controlled for with optimal model utility, proposing a pre-processing algorithm called FairRR that yields excellent downstream model utility and fairness.
Paper Structure (15 sections, 1 theorem, 18 equations, 2 figures, 3 tables)

This paper contains 15 sections, 1 theorem, 18 equations, 2 figures, 3 tables.

Table of Contents

  1. INTRODUCTION
  2. PRELIMINARIES
  3. Fairness
  4. Fair Bayes Optimal Classifiers under Demographic Parity
  5. Design Matrices in Randomized Response
  6. METHOD
  7. Overview
  8. Fairness through Randomized Response
  9. Randomized Response and the Fair Bayes-Optimal Classifier
  10. FairRR: a Randomized Response Mechanism for Fair Classification
  11. EXPERIMENTS
  12. Empirical Data Analysis
  13. Results
  14. DISCUSSION
  15. CONCLUSION

Key Result

Theorem 3.1

Let $(X,A,Y)$ follow a distribution $\mathbb{P}$ on $\mathcal{X}\times \{0,1\}\times \{0,1\}$. Consider a group-wise im-balanced randomized response mechanism $\widetilde{Y}=\mathcal{R}_{\theta_{11},\theta_{10},\theta_{01},\theta_{00}}(A,Y)$ with, for $a\in\{0,1\}$, When the flipping probabilities satisfy: where $T_1(\cdot)$, $T_0(\cdot)$ and $t^\star$ are the same as in eq:FBOC. Denote $\wideti

Figures (2)

  • Figure 1: Logistic Regression Accuracy/ Disparity Trade-offs: FairRR and FAWOS comparison across datasets.
  • Figure 2: Accuracy/ Disparity Pareto Curves of various pre-processing algorithms on the Adult dataset evaluated with Support Vector Machines.

Theorems & Definitions (8)

  • Definition 2.1: Demographic Parity
  • Definition 2.2: Equality of Opportunity
  • Definition 2.3: Predictive Equality
  • Theorem 3.1
  • Remark 3.2
  • Definition 3.3: Demographic Parity
  • Definition 3.4: Equality of Opportunity
  • Definition 3.5: Predictive Equality