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Statistical Inference for Fairness Auditing
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Frames fairness auditing as multiple hypothesis testing and uses bootstrap-based simultaneous lower confidence bounds and FWER/FDR-controlled flagging to certify or flag performance disparities over many (even infinite) subpopulations and covariate shifts.
Problem
Auditing a black-box model's performance disparities across many, possibly intersectional or infinite, subpopulations with statistical guarantees, using only held-out predictions.
Approach
Bootstrap the supremum of a size-rescaled disparity process (multiplying by group probability and a shrunken scale estimate) so that simultaneous lower confidence bounds and FWER/FDR-controlled flags remain valid even for small groups; extend to RKHS-ball covariate shifts via a top-eigenvalue reduction.
Key results
- On synthetic experiments, the rescaled bootstrap confidence bounds achieve about 0.84-0.91 simultaneous coverage at nominal 0.9 for n between 100 and 1600.
- On Folktables, the FDR of BH flags stays below the nominal 0.1 at every sample size (e.g., 0.045 at n=100 for task 1).
- On COMPAS, the audit certifies that African-American defendants have at least 1.87% higher PPV than Caucasian defendants at 90% lower confidence.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply the RKHS bootstrap confidence-bound audit over Gaussian RKHS tilts | RKHS confidence bound · Synthetic RKHS audit | realized percentile | Mixed |
| Apply BH flagging to Folktables task 1 | Folktables income prediction · Folktables task 1 | FDR: 0.045, 0.038, 0.032, 0.025, 0.021, 0.014 | Helped |
| Apply BH flagging to Folktables task 2 despite violating stated assumptions | Folktables income prediction · Folktables task 2 | FDR: 0.003, 0.005, 0.003, 0.004, 0.003, 0.004 | Helped |
| Apply BH flagging to Folktables task 3 despite violating stated assumptions | Folktables income prediction · Folktables task 3 | FDR: 0.0, 0.0, 0.0, 0.0, 0.0, 0.002 | Helped |
| Use the rescaled rather than unscaled confidence-bound procedure (ablation) | Synthetic confidence-set certification · Synthetic sub-interval certification | power | Helped |
| Estimate group-adaptive variance with finite w0 rather than use w0 = ∞ (ablation) | Rescaled certification · Finite-sample confidence bounds | validity | Hurt |
Surprising findings
- Estimating the asymptotic variance in the rescaling can harm finite-sample validity, so the authors recommend w0 = infinity.
- The unscaled bootstrap lower bound is conservative and has low power for small groups, and the RKHS bootstrap can be conservative at small sample sizes.
Limitations
- Simultaneous validity is asymptotic; finite-sample guarantees are conservative or require further work.
- FWER for Boolean certification is only exactly alpha when the disparity equals the threshold on all groups.
- Rescaled RKHS bootstrap is computationally prohibitive, so only the unscaled version is practical.
Experimental setup
Datasets: COMPAS (ProPublica 2016) Folktables 2018 ACS California synthetic linear and heteroskedastic models synthetic CQR dataset
Benchmarks: COMPAS Folktables
Metrics: FWER power simultaneous coverage FDR false positive rate disparity PPV disparity
Baselines: Bonferroni correction unscaled bootstrap lower bound
Builds on: Benjamini-Hochberg procedure conformalized quantile regression Folktables
Closest papers by meaning
- Cost Efficient Fairness Audit Under Partial Feedback (NeurIPS 2026 · similarity 0.83)
- Robust ML Auditing using Prior Knowledge (ICML 2025 · similarity 0.82)
- Sequentially Auditing Differential Privacy (NeurIPS 2025 · similarity 0.81)
- Fairness Shields: Safeguarding against Biased Decision Makers (AAAI 2025 · similarity 0.80)
- Size-adaptive Hypothesis Testing for Fairness (NeurIPS 2025 · similarity 0.80)
- FairPFN: A Tabular Foundation Model for Causal Fairness (ICML 2025 · similarity 0.80)
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