Research map / Learning theory and algorithms / Fairness
Fairness-aware Bayes Optimal Functional Classification
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Proposes a Bayes-optimal fairness-constrained classifier for functional data via Radon-Nikodym derivatives and a post-processing Fair-FLDA algorithm for Gaussian processes with group-wise thresholding, with finite-sample fairness and excess-risk guarantees.
Problem
Classifying functional data under fairness constraints (bounded disparity of opportunity, predictive or demographic disparity) while minimising misclassification error, with unknown covariance eigenstructure in infinite-dimensional function spaces.
Approach
Replaces posterior probabilities (intractable in function space) with Radon-Nikodym derivatives, uses the generalised Neyman-Pearson lemma to derive group-wise thresholds for bilinear disparity measures, and estimates them via a truncated functional LDA plug-in with calibration on held-out data.
Key results
- Fair-FLDA keeps median disparity near the target delta while FLDA violates fairness; Fair-FLDAc (calibrated) gives median disparity strictly below delta in simulations.
- On NHANES, Fair-FLDA and Fair-FLDAc classification errors remain comparable to unconstrained FLDA while controlling median disparity.
- Theory: excess risk of Fair-FLDA bounded by (eps_pi+eps_eta+eps_tau)^2 plus a cost-of-fairness term; for DO with suitable truncation J, excess risk rate O_p(N^{(alpha-2beta+1)/(2alpha+2)}) in one regime.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply group-wise thresholding to enforce fairness constraints | Fair-FLDA vs FLDA · Simulated data; disparity of opportunity (DO), predictive disparity (PD), and demographic disparity (DD) | classification error | No clear effect |
| Apply group-wise thresholding to enforce fairness constraints | Fair-FLDA vs FLDA · NHANES | classification error | No clear effect |
| Apply group-wise thresholding to enforce fairness constraints | Fair-FLDA vs FLDA · Simulated data; DO, PD, and DD | disparity | Helped |
| Use the calibrated Fair-FLDA variant instead of Fair-FLDA | Fair-FLDA_c · Simulated data; DO, PD, and DD | 95% disparity quantile | Helped |
| Use the default calibration constant in Fair-FLDA_c | Fair-FLDA_c · NHANES; DO | 95% disparity quantile | Hurt |
| Tune the calibration parameter κ to keep the empirical 1−ρ disparity quantile below δ | Fair-FLDA_c · NHANES | disparity control | Helped |
| Increase the fairness tolerance δ | Fair-FLDA and Fair-FLDA_c · Simulated data; DO, PD, and DD | classification error | Helped |
| Increase the sample size n | Fair-FLDA and Fair-FLDA_c · Simulated Gaussian data; DO, PD, and DD | excess risk | Helped |
| Increase mean-difference alignment β | Fair-FLDA and Fair-FLDA_c · Simulated Gaussian data | excess risk | Helped |
| Use β=2 rather than β=1.5 | Fair-FLDA and Fair-FLDA_c · Simulated Gaussian data | classification error | Hurt |
| Apply the Gaussian-derived classifier when the data are non-Gaussian | Fair-FLDA and Fair-FLDA_c · Simulated non-Gaussian data; DO, PD, and DD | disparity control | Helped |
| Apply fairness-aware thresholding in the automatically fair perfect-classification setting | Fair-FLDA and Fair-FLDA_c · Simulated perfect-classification data; DO and PD under setting I | disparity | Helped |
Surprising findings
- Under perfect classification with DD in one setting, |DD(tau)| stays at 0.3 for all tau, so lower disparity is infeasible.
- Fair-FLDA's 95% disparity quantile can slightly exceed delta, so calibration is needed for probabilistic control.
Limitations
- Theory restricted to homoscedastic Gaussian processes with continuous trajectories and fully observed functions
- Requires sensitive attribute available at training and prediction time
- Radon-Nikodym derivative must be tractable; approximations are not analysed
Experimental setup
Datasets: NHANES 2005-2006 accelerometer intensity data synthetic Gaussian functional data
Benchmarks: NHANES 2005-2006 (real) synthetic Gaussian functional classification
Metrics: misclassification error disparity of opportunity predictive disparity demographic disparity 95% quantile of unfairness
Baselines: FLDA oracle fair Bayes classifier
Builds on: generalised Neyman-Pearson lemma fair classification functional linear discriminant analysis Gaussian measure theory (Feldman-Hajek)
Closest papers by meaning
- FedFACT: A Provable Framework for Controllable Group-Fairness Calibration in Federated Learning (NeurIPS 2025 · similarity 0.87)
- f-FERM: A Scalable Framework for Robust Fair Empirical Risk Minimization (ICLR 2024 · similarity 0.87)
- On the Maximal Local Disparity of Fairness-Aware Classifiers (ICML 2024 · similarity 0.87)
- Efficient Fairness-Performance Pareto Front Computation (NeurIPS 2025 · similarity 0.87)
- Kernel-based Equalized Odds: A Quantification of Accuracy-Fairness Trade-off in Fair Representation Learning (NeurIPS 2025 · similarity 0.87)
- Post-hoc bias scoring is optimal for fair classification (ICLR 2024 · similarity 0.86)
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