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Fair Classification by Direct Intervention on Operating Characteristics

Kevin Jiang, Edgar Dobriban

TL;DR

This paper tackles the challenge of achieving approximate group fairness in binary classification under multiple linear fractional constraints by shifting the problem to the space of operating characteristics. It introduces ROCF, a post-processing framework that leverages the convex hull geometry of group-wise ROC curves to identify target operating characteristics and then constructs a randomized mixed-GWTR post-processor to match those targets. The method employs rate-space reformulation, centroid-based linearization, and a two-stage optimization (inner LPs/outer centroid search) to handle multiple protected attributes and LF constraints, with empirical validation on COMPAS and ACSIncome showing near-oracle accuracy and low intervention rates. The results indicate that complex fairness requirements can be met in practice without large drops in accuracy, highlighting the practical viability of post-processing ROC-focused interventions for fair classification in high-stakes settings.

Abstract

We develop new classifiers under group fairness in the attribute-aware setting for binary classification with multiple group fairness constraints (e.g., demographic parity (DP), equalized odds (EO), and predictive parity (PP)). We propose a novel approach, applicable to linear fractional constraints, based on directly intervening on the operating characteristics of a pre-trained base classifier, by (i) identifying optimal operating characteristics using the base classifier's group-wise ROC convex hulls and (ii) post-processing the base classifier to match those targets. As practical post-processors, we consider randomizing a mixture of group-wise thresholding rules subject to minimizing the expected number of interventions. We further extend our approach to handle multiple protected attributes and multiple linear fractional constraints. On standard datasets (COMPAS and ACSIncome), our methods simultaneously satisfy approximate DP, EO, and PP with few interventions and a near-oracle drop in accuracy; comparing favorably to previous methods.

Fair Classification by Direct Intervention on Operating Characteristics

TL;DR

This paper tackles the challenge of achieving approximate group fairness in binary classification under multiple linear fractional constraints by shifting the problem to the space of operating characteristics. It introduces ROCF, a post-processing framework that leverages the convex hull geometry of group-wise ROC curves to identify target operating characteristics and then constructs a randomized mixed-GWTR post-processor to match those targets. The method employs rate-space reformulation, centroid-based linearization, and a two-stage optimization (inner LPs/outer centroid search) to handle multiple protected attributes and LF constraints, with empirical validation on COMPAS and ACSIncome showing near-oracle accuracy and low intervention rates. The results indicate that complex fairness requirements can be met in practice without large drops in accuracy, highlighting the practical viability of post-processing ROC-focused interventions for fair classification in high-stakes settings.

Abstract

We develop new classifiers under group fairness in the attribute-aware setting for binary classification with multiple group fairness constraints (e.g., demographic parity (DP), equalized odds (EO), and predictive parity (PP)). We propose a novel approach, applicable to linear fractional constraints, based on directly intervening on the operating characteristics of a pre-trained base classifier, by (i) identifying optimal operating characteristics using the base classifier's group-wise ROC convex hulls and (ii) post-processing the base classifier to match those targets. As practical post-processors, we consider randomizing a mixture of group-wise thresholding rules subject to minimizing the expected number of interventions. We further extend our approach to handle multiple protected attributes and multiple linear fractional constraints. On standard datasets (COMPAS and ACSIncome), our methods simultaneously satisfy approximate DP, EO, and PP with few interventions and a near-oracle drop in accuracy; comparing favorably to previous methods.

Paper Structure

This paper contains 46 sections, 1 theorem, 37 equations, 2 figures, 9 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Our contributions.
  3. Related Work
  4. Problem Setup
  5. Fair classification via ROC feasibility regions
  6. Fair classification via operating characteristic feasibility regions (ROCF).
  7. Rate-space reformulation & Post-processing Condition
  8. Operating characteristic Feasibility Regions and Centroid-based linearization
  9. Linear constraints via centroids.
  10. Linear--fractional constraints via fixed centroids.
  11. Inner linear program for fixed linear fractional centroids.
  12. Outer search over linear fractional centroids.
  13. Constructing classifiers
  14. Randomization procedure
  15. Experimental Results
  16. ...and 31 more sections

Key Result

Theorem 4.1

Define the value function $\Phi$ such that $\Phi(\vec{q})$ is the optimal objective value of equation eq:linear-opt-prob for any $\vec{q} \in \mathbb{R}^{|\mathcal{K}_{\mathrm{LF}}|}$. Then, the value of the optimization problem from equation eq:post-processing-function-opt-problem is equal to $\min

Figures (2)

  • Figure 1: CPU runtime (mean $\pm$ s.e., seconds) for (A) COMPAS, (B) ACSIncome ($|\mathcal{A}|{=}2$), and (C) ACSIncome ($|\mathcal{A}|{=}5$). As in §\ref{['sec:exp:primary-result']} and §\ref{['sec:exp:multiple-protected-attributes']}, the disparities $\delta_{\textrm{DP}},\delta_{\textrm{EOpp}},\delta_{\textrm{PEq}}$ and $\delta_{\textrm{PP}}$ are controlled at level $0.05$ whenever active.
  • Figure 2: CPU runtime (mean $\pm$ s.e., seconds) for (A) COMPAS, (B) ACSIncome ($|\mathcal{A}|{=}2$), and (C) ACSIncome ($|\mathcal{A}|{=}5$). As in §\ref{['sec:exp:multiple-LF-constraints']}, the disparities $\delta_{\textrm{EOpp}},\delta_{\textrm{PP}}$ and $\delta_{\textrm{FOR-parity}}$ are controlled at level $0.05$ for our methods ROCF-AD/LF, while LPP-EOpp only controls for equality of opportunity.

Theorems & Definitions (9)

  • Definition 3.1: LF group performance functions
  • Definition 3.2: Mixed-GWTR
  • Theorem 4.1
  • Remark 4.2
  • Remark A.1
  • Remark A.2
  • Definition A.3: Interventions
  • Definition A.4: Minimal intervention
  • Definition A.5: Operating characteristic feasibility region