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Post-hoc bias scoring is optimal for fair classification
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Derives the Bayes-optimal classifier under composite group-fairness constraints (DP, EOp, EO) as a linear modification of the unconstrained classifier via instance-level bias scores, and proposes MBS, a post-hoc method that needs no test-time sensitive attribute.
Problem
Adjusting a binary classifier to satisfy group fairness constraints (DP, EOp, EO, composite criteria) while maintaining accuracy, without requiring sensitive attributes at inference time.
Approach
Characterizes the Bayes-optimal fair classifier as a modification of the unconstrained classifier by flipping predictions where a linear rule over K instance-level bias scores (ratio of fairness contribution to confidence) exceeds 1; the fitted rule uses auxiliary estimated p(Y|X) and p(A|X) or p(Y,A|X) so test sensitive attributes are not needed.
Key results
- On CelebA EO constraint with delta=5%, MBS reaches 80.1% accuracy with 2.2% EO on (a,m), versus 71.7% / 3.8% for the strongest in-processing baseline row.
- Under EO constraints on CelebA, MBS consistently achieves better or competitive accuracy than the Z17-style baseline, which loses accuracy across all six tasks.
- Ablations show test DP stays near the target delta and accuracy drops within about 1% when the auxiliary p(Y|X) and p(A|X) are corrupted.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use post-hoc Modification with Bias Scores (MBS) instead of Z17 | Fair classification on Adult Census and COMPAS under DP · Adult Census and COMPAS | accuracy at comparable DP constraints | Helped |
| Use MBS instead of Z17 | Fair classification on Adult Census and COMPAS under EO · Adult Census and COMPAS | accuracy-EO trade-off | Helped |
| Use MBS instead of the other compared method | CelebA fair attribute classification under EO · CelebA, six target-sensitive attribute tasks | accuracy-EO trade-off | Helped |
| Add uniform noise to estimated p(Y|X) and p(A|X) (ablation) | MBS under DP · Adult Census and CelebA (Attractive, Male) | test accuracy: within 1% across most α's | Hurt |
| Train the sensitive-attribute model with stronger weight decay (ablation) | MBS under DP · CelebA (Attractive, Male) | post-processed target accuracy | No clear effect |
| Train the sensitive-attribute model with stronger weight decay (ablation) | MBS under DP · CelebA (Attractive, Male) | DP | No clear effect |
Surprising findings
- Under EO, the optimal modification is not characterized by a unique scalar bias score, so some points flipped at a looser constraint are unflipped at a tighter one.
- On COMPAS, the post-hoc method underperforms a baseline because the small dataset makes estimating p(Y|X) and p(A|X) unreliable.
Limitations
- Requires accurate auxiliary estimates of p(Y|X) and p(A|X) or p(Y,A|X); small datasets such as COMPAS degrade performance.
- Under EO, no unique scalar bias score exists, so the method needs to fit a 2-parameter linear rule on validation data.
- Theoretical guarantees assume ground-truth-like conditionals, with error bounds only informal.
Experimental setup
Datasets: Adult Census COMPAS CelebA
Benchmarks: Adult Census COMPAS CelebA
Metrics: accuracy demographic parity equalized odds
Baselines: Zafar et al. 2017 (Z17) Jiang et al. 2019 Wasserstein fair classification (J19) Hardt et al. 2016 (H16) post-processing Park et al. 2022 fair contrastive learning (P22)
Builds on: Hardt et al. 2016 equality of opportunity Menon & Williamson 2018 cost-sensitive fairness Neyman-Pearson lemma
Closest papers by meaning
- Fair Classification by Direct Intervention on Operating Characteristics (ICLR 2026 · similarity 0.91)
- Fair and Optimal Classification via Post-Processing (ICML 2023 · similarity 0.91)
- Bayes-Optimal Fair Classification with Multiple Sensitive Features (AAAI 2026 · similarity 0.90)
- How Far Can Fairness Constraints Help Recover From Biased Data? (ICML 2024 · similarity 0.88)
- A Sequentially Fair Mechanism for Multiple Sensitive Attributes (AAAI 2024 · similarity 0.87)
- FairWASP: Fast and Optimal Fair Wasserstein Pre-processing (AAAI 2024 · similarity 0.87)
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