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Overcoming Representation Bias in Fairness-Aware data Repair using Optimal Transport

Abigail Langbridge, Anthony Quinn, Robert Shorten

TL;DR

A novel definition of the fair distributional target, along with quantifiers that allow us to trade fairness against damage in the transformed data, are formulated and used to reveal excellent performance of the representation-bias-tolerant scheme in simulated and benchmark data sets.

Abstract

Optimal transport (OT) has an important role in transforming data distributions in a manner which engenders fairness. Typically, the OT operators are learnt from the unfair attribute-labelled data, and then used for their repair. Two significant limitations of this approach are as follows: (i) the OT operators for underrepresented subgroups are poorly learnt (i.e. they are susceptible to representation bias); and (ii) these OT repairs cannot be effected on identically distributed but out-of-sample (i.e.\ archival) data. In this paper, we address both of these problems by adopting a Bayesian nonparametric stopping rule for learning each attribute-labelled component of the data distribution. The induced OT-optimal quantization operators can then be used to repair the archival data. We formulate a novel definition of the fair distributional target, along with quantifiers that allow us to trade fairness against damage in the transformed data. These are used to reveal excellent performance of our representation-bias-tolerant scheme in simulated and benchmark data sets.

Overcoming Representation Bias in Fairness-Aware data Repair using Optimal Transport

TL;DR

A novel definition of the fair distributional target, along with quantifiers that allow us to trade fairness against damage in the transformed data, are formulated and used to reveal excellent performance of the representation-bias-tolerant scheme in simulated and benchmark data sets.

Abstract

Optimal transport (OT) has an important role in transforming data distributions in a manner which engenders fairness. Typically, the OT operators are learnt from the unfair attribute-labelled data, and then used for their repair. Two significant limitations of this approach are as follows: (i) the OT operators for underrepresented subgroups are poorly learnt (i.e. they are susceptible to representation bias); and (ii) these OT repairs cannot be effected on identically distributed but out-of-sample (i.e.\ archival) data. In this paper, we address both of these problems by adopting a Bayesian nonparametric stopping rule for learning each attribute-labelled component of the data distribution. The induced OT-optimal quantization operators can then be used to repair the archival data. We formulate a novel definition of the fair distributional target, along with quantifiers that allow us to trade fairness against damage in the transformed data. These are used to reveal excellent performance of our representation-bias-tolerant scheme in simulated and benchmark data sets.
Paper Structure (19 sections, 20 equations, 5 figures, 5 tables)

This paper contains 19 sections, 20 equations, 5 figures, 5 tables.

Table of Contents

  1. Introduction
  2. AI Unfairness and Representation Bias
  3. Societal and AI Unfairness
  4. Representation Bias
  5. Bayesian Learning of the Sub-Group Models, $\mathsf{F}_{u,s}$
  6. Data-Driven Fairness Correction
  7. Learning the Repair Operation
  8. Evaluating (Un)Fairness
  9. Data Damage
  10. Experiments
  11. Learning non-Gaussian Models
  12. Multinomial Models
  13. Gaussian Mixture Models
  14. Fairness Repair Under Representation Bias
  15. Benchmarking on Simulated and Real Data
  16. ...and 4 more sections

Figures (5)

  • Figure 1: Comparison of the causal graphs of different sources of unfairness under our conditional independence model.
  • Figure 2: LKLD until stopping for observations from categorical variables with $q$ states.
  • Figure 3:
  • Figure 4: Stopping numbers, $\hat{n}$, sample mean, $\mathbb{E}(X)$, and sample variance, $S^2(X)$, for GMM data over 500 Monte-Carlo simulations.
  • Figure 5: $\log \hat{E}$ and damage (Definition \ref{['def:kld_damage']}) for data with simulated representation bias $Pr[U = 0] \in (0, 0.5]$. Results are reported $\pm$ standard deviation over 20 Monte-Carlo simulations.

Theorems & Definitions (2)

  • Definition 2.1: Representation bias
  • Definition 4.1