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Shapley meets Rawls: an integrated framework for measuring and explaining unfairness

Fadoua Amri-Jouidel, Emmanuel Kemel, Stéphane Mussard

Abstract

Explainability and fairness have mainly been considered separately, with recent exceptions trying the explain the sources of unfairness. This paper shows that the Shapley value can be used to both define and explain unfairness, under standard group fairness criteria. This offers an integrated framework to estimate and derive inference on unfairness as-well-as the features that contribute to it. Our framework can also be extended from Shapley values to the family of Efficient-Symmetric-Linear (ESL) values, some of which offer more robust definitions of fairness, and shorter computation times. An illustration is run on the Census Income dataset from the UCI Machine Learning Repository. Our approach shows that ``Age", ``Number of hours" and ``Marital status" generate gender unfairness, using shorter computation time than traditional Bootstrap tests.

Shapley meets Rawls: an integrated framework for measuring and explaining unfairness

Abstract

Explainability and fairness have mainly been considered separately, with recent exceptions trying the explain the sources of unfairness. This paper shows that the Shapley value can be used to both define and explain unfairness, under standard group fairness criteria. This offers an integrated framework to estimate and derive inference on unfairness as-well-as the features that contribute to it. Our framework can also be extended from Shapley values to the family of Efficient-Symmetric-Linear (ESL) values, some of which offer more robust definitions of fairness, and shorter computation times. An illustration is run on the Census Income dataset from the UCI Machine Learning Repository. Our approach shows that ``Age", ``Number of hours" and ``Marital status" generate gender unfairness, using shorter computation time than traditional Bootstrap tests.

Paper Structure

This paper contains 21 sections, 10 theorems, 94 equations, 1 figure, 6 tables.

Table of Contents

  1. Introduction
  2. Group fairness and explainability: separate literature streams
  3. Group fairness criteria
  4. Explainability with the Shapley value
  5. Shapley for Fairness and Explainability
  6. Group level explainability
  7. Equivalences: First-stage Shapley
  8. Equivalences: Two-stage Shapley
  9. Additional results: robustness, inference and implementability
  10. Fairness explanation under ESL
  11. Application on Census Data
  12. Application of the main theorems
  13. Computation times
  14. Fairness mitigation
  15. Conclusion
  16. ...and 6 more sections

Key Result

Theorem 3.1

Let $f_t$ be a binary classifier and $\varphi^{Sh}$ the Shapley value. Equivalences: (i)$f_t$ respects (IND)$\Leftrightarrow$$\varphi_{g=1}^{Sh}(\mathbf{X}, v^{(SR)}) = \varphi_{g=2}^{Sh}(\mathbf{X}, v^{(SR)})$ (ii)$f_t$ respects (SEP)$\Leftrightarrow \left\{\right.$ (iii)$f_t$ respects (SUF)$\Leftr

Figures (1)

  • Figure 1: Two-stage Shapley attribution method

Theorems & Definitions (21)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Theorem 3.1: Group Fairness $\Leftrightarrow$ Shapley
  • proof
  • Proposition 3.1: Two-stage Shapley
  • proof
  • Remark 3.1
  • Proposition 4.1
  • Theorem 4.1: Group Fairness $\Leftrightarrow$ ESL value
  • ...and 11 more