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On the Maximal Local Disparity of Fairness-Aware Classifiers
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Proposes MCDP(ε), a fairness metric measuring the maximal local CDF disparity between groups over ε-neighborhoods of predictions, with exact and approximate estimators and a bi-level DiffMCDP training method.
Problem
Existing demographic parity metrics (ΔDP, ABCC) average out extreme local disparities in model prediction distributions between demographic groups, so they can misjudge fairness violations.
Approach
Measure fairness as the maximum over prediction points of the minimal CDF disparity within an ε-neighborhood (MCDP(ε)), prove properties and bounds, provide exact and sampling-based estimators, and train with a differentiable temperature-sigmoid approximation of MCDP(0) in a bi-level optimization.
Key results
- On Adult, DiffMCDP reduces MCDP(0) to 11.53 vs 21.18 for the next best (DiffABCC) and 36.62 for ERM, with AP 73.90.
- On Bank, DiffMCDP achieves the lowest ABCC (1.83) and MCDP(0) (11.02) among methods, with AP 59.98.
- The approximate algorithm at K=32 reports 0.03%-3% average relative error with over 1000x efficiency improvement over the exact algorithm (as stated in the paper).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Regularize differentiable MCDP(0) instead of using the baseline training objectives | DiffMCDP versus baselines · Adult, Bank, CelebA-A, CelebA-W | MCDP(0): Adult: 21.18 ± 1.23 -> 11.53 ± 1.12; Bank: 13.22 ± 2.91 -> 11.02 ± 1.00; CelebA-A: 27.38 ± 2.46 -> 23.10 ± 1.66; CelebA- | Helped |
| Regularize differentiable MCDP(0) instead of using baseline training objectives | DiffMCDP versus baselines · Adult and Bank | ABCC: Adult: 7.34 ± 0.62 -> 6.09 ± 0.59; Bank: 1.98 ± 0.23 -> 1.83 ± 0.28 | Helped |
| Regularize differentiable MCDP(0) instead of using baseline training objectives | DiffMCDP versus baselines · CelebA-A and CelebA-W | ΔDP: CelebA-A: 26.36 ± 2.48 -> 21.10 ± 1.94; CelebA-W: 19.93 ± 1.85 -> 19.58 ± 1.91 | Helped |
| Use DiffMCDP rather than ERM, with fairness regularization | Classifier training · Adult, Bank, CelebA-A, CelebA-W | AP: Adult: 76.77 ± 0.54 -> 73.90 ± 0.29; Bank: 61.02 ± 1.12 -> 59.98 ± 1.80; CelebA-A: 84.62 ± 0.38 -> 80.32 ± 0.67; CelebA- | Hurt |
| Use moderate temperature τ=10 or 20 instead of very small or large temperatures τ=5 or 50 (ablation) | DiffMCDP · Adult and Bank | Fairness-accuracy trade-off | Helped |
| Increase sampling frequency K in the approximate MCDP calculation (ablation) | Approximate MCDP calculation · Real-world datasets | Relative estimation error: when K=32, the average estimation error ... are 0.03%-3% | Helped |
| Increase sampling frequency K in the approximate MCDP calculation (ablation) | Approximate MCDP calculation · Real-world datasets | Calculation time | Hurt |
| Increase ε in the approximate MCDP calculation (ablation) | Approximate MCDP calculation · Real-world datasets | Relative estimation error | Hurt |
| Increase ε in the approximate MCDP calculation (ablation) | Approximate MCDP calculation · Real-world datasets | Efficiency improvement over exact calculation | Helped |
| Regularize MCDP(0) rather than ΔDP | DiffMCDP versus DiffDP · Bank | MCDP(0): 47.98% | Helped |
Surprising findings
- Methods that reach the lowest ΔDP (e.g., FairMixup on Adult) can have substantially higher MCDP(0) than DiffMCDP, showing expectation-level metrics can miss local disparity.
- Relative ranking of fairness methods changes with the neighborhood size ε, so single-ε evaluation can be misleading.
Limitations
- Only demographic parity with binary sensitive attributes and binary classification is studied.
- Gradient vanishing at large temperature limits the differentiable approximation; temperature must be tuned.
- Approximate algorithm error grows with ε.
Experimental setup
Datasets: Adult Bank CelebA
Benchmarks: Adult Bank CelebA-A CelebA-W
Metrics: AP ΔDP ABCC MCDP(0) MCDP(ε)
Baselines: ERM AdvDebias DiffDP FairMixup DRAlign DiffABCC
Builds on: ABCC FairMixup DRAlign AdvDebias
Closest papers by meaning
- Fairness via Independence: A General Regularization Framework for Machine Learning (ICLR 2026 · similarity 0.89)
- Geometry of Relaxed Fair Regression: A Unified Framework for Aware and Unaware Settings (NeurIPS 2026 · similarity 0.88)
- On the Fairness ROAD: Robust Optimization for Adversarial Debiasing (ICLR 2024 · similarity 0.88)
- The Fragility of Fairness: Causal Sensitivity Analysis for Fair Machine Learning (NeurIPS 2024 · similarity 0.87)
- Fairness-aware Bayes Optimal Functional Classification (NeurIPS 2025 · similarity 0.87)
- Fairness without Demographics through Shared Latent Space-Based Debiasing (AAAI 2024 · similarity 0.87)
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