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Optimisation Strategies for Ensuring Fairness in Machine Learning: With and Without Demographics

Quan Zhou

TL;DR

An extensive overview of this field is provided and a framework for a group-blind bias-repair is introduced, aiming to mitigate bias without relying on sensitive attributes, ensuring the robustness and reliability of the proposed methodologies.

Abstract

Ensuring fairness has emerged as one of the primary concerns in AI and its related algorithms. Over time, the field of machine learning fairness has evolved to address these issues. This paper provides an extensive overview of this field and introduces two formal frameworks to tackle open questions in machine learning fairness. In one framework, operator-valued optimisation and min-max objectives are employed to address unfairness in time-series problems. This approach showcases state-of-the-art performance on the notorious COMPAS benchmark dataset, demonstrating its effectiveness in real-world scenarios. In the second framework, the challenge of lacking sensitive attributes, such as gender and race, in commonly used datasets is addressed. This issue is particularly pressing because existing algorithms in this field predominantly rely on the availability or estimations of such attributes to assess and mitigate unfairness. Here, a framework for a group-blind bias-repair is introduced, aiming to mitigate bias without relying on sensitive attributes. The efficacy of this approach is showcased through analyses conducted on the Adult Census Income dataset. Additionally, detailed algorithmic analyses for both frameworks are provided, accompanied by convergence guarantees, ensuring the robustness and reliability of the proposed methodologies.

Optimisation Strategies for Ensuring Fairness in Machine Learning: With and Without Demographics

TL;DR

An extensive overview of this field is provided and a framework for a group-blind bias-repair is introduced, aiming to mitigate bias without relying on sensitive attributes, ensuring the robustness and reliability of the proposed methodologies.

Abstract

Ensuring fairness has emerged as one of the primary concerns in AI and its related algorithms. Over time, the field of machine learning fairness has evolved to address these issues. This paper provides an extensive overview of this field and introduces two formal frameworks to tackle open questions in machine learning fairness. In one framework, operator-valued optimisation and min-max objectives are employed to address unfairness in time-series problems. This approach showcases state-of-the-art performance on the notorious COMPAS benchmark dataset, demonstrating its effectiveness in real-world scenarios. In the second framework, the challenge of lacking sensitive attributes, such as gender and race, in commonly used datasets is addressed. This issue is particularly pressing because existing algorithms in this field predominantly rely on the availability or estimations of such attributes to assess and mitigate unfairness. Here, a framework for a group-blind bias-repair is introduced, aiming to mitigate bias without relying on sensitive attributes. The efficacy of this approach is showcased through analyses conducted on the Adult Census Income dataset. Additionally, detailed algorithmic analyses for both frameworks are provided, accompanied by convergence guarantees, ensuring the robustness and reliability of the proposed methodologies.

Paper Structure

This paper contains 93 sections, 25 theorems, 177 equations, 18 figures, 9 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Societal Impacts of Machine Learning
  3. Initiatives to Address Bias
  4. Contributions of the Thesis
  5. Proper Learning of Linear Dynamic Systems (Chapter \ref{['cha:tac']}):
  6. Fairness in Forecast for Imbalanced Data (Chapter \ref{['cha:jair']}):
  7. Group-Blind Transport Map for Unavailable Sensitive Attributes (Chapter \ref{['cha:ot']}):
  8. Structure of the Thesis
  9. Publications
  10. Preliminaries in Machine Learning Fairness
  11. Fairness Definitions
  12. Group Fairness Definitions
  13. Individual Fairness Definitions
  14. Common Approaches and Open Questions
  15. Proxies of Sensitive Attributes
  16. ...and 78 more sections

Key Result

Theorem 3.1

For any observable linear system $(G,F,V,W)$, for any length $T$ of a time window, and any error $\epsilon > 0$, under the Archimedean assumption, detailed in Theorem the:positivetrace2cyclic, there is a convex optimisation problem whose objective function value is at most $\epsilon$ away from Equat

Figures (18)

  • Figure 1: Structure of the chapters in the thesis
  • Figure 2: Left: The fit values \ref{['NRMSE']} of $81$ experiments of our method at different combinations of noise standard deviations of process noise $W$ and observation noise $V$ and Right: at different combinations of parameters $\lambda_1$ and $\lambda_2$. Both use the data generated from systems in \ref{['equ:LDS']}. Lighter colours indicate higher fit values and thus better simulation performance.
  • Figure 3: The fit values \ref{['NRMSE']} of our method compared to the leading system identification methods implemented in Matlab™ System Identification Toolbox™. Upper: the mean (solid lines) and mean $\pm$ one standard deviations (dashed lines) of fit values as standard deviation of both process noise and observation noise increasing in lockstep from $0.1$ to $0.9$. The time series used for simulation are generated from systems in \ref{['equ:LDS']} (left) and higher differential order systems in \ref{['equ:LDS-higher']} (right), with the dimensions $k$ of both systems being $2$. Lower: the mean (solid dots) and mean $\pm$ one standard deviations (vertical error bars) of fit values at different dimensions $k$ of the underlying systems in \ref{['equ:LDS']}. Higher fit values indicate better simulation performance.
  • Figure 4: Left: The time series of stock price (dark) for the 21$^\textrm{st}$-121$^\textrm{st}$ period used in arima_aaai, and the predicted outputs of our method (yellow) compared against "least squares auto" (blue) implemented in Matlab™ System Identification Toolbox™. The estimated dimension $\hat{k}$ of "least squares auto" is iterated from $1$ to the highest number of $4$. The percentages in legend are corresponding fit values of one-step predictions. Right: a zoom-in for the 66$^\textrm{th}$-101$^\textrm{st}$ period.
  • Figure 5: Left: The (solid or dashed) curves show the mean runtime of the SDP relaxation of the baseline "least squares auto" (blue), the TSSOS hierarchy (green) and the NPA hierarchy (yellow), at different moment orders $d$ or estimated dimensions $\hat{k}$. The mean $\pm$ one standard deviation of runtime is displayed by shaded error bands. Upper-right: The mean and mean $\pm$ one standard deviation of runtime of the SDP relaxation of TSSOS hierarchy at moment order $d=1$ and the "least squares auto" with dimension $\hat{k}=1$. Lower-right: The red bars display the sparsity of NPA hierarchy of the experiment on stock-market data against the length of time window, by ratios of non-zero coefficients out of all coefficients in the SDP relaxations
  • ...and 13 more figures

Theorems & Definitions (76)

  • Theorem 3.1
  • proof
  • Example 5.1
  • Example 5.2
  • Definition 5.1: a sensitive attribute
  • Definition 5.2: Source variables of a neutral attribute
  • Definition 5.3: Target variables of the neutral attribute
  • Definition 5.4: Projection
  • Example 5.3
  • Example 5.4
  • ...and 66 more