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Bridging Fairness and Efficiency in Conformal Inference: A Surrogate-Assisted Group-Clustered Approach
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Proposes SAGCCI, a conformal prediction framework that clusters protected groups by similar conformal score distributions and uses an efficient influence function with surrogate outcomes to produce narrower group-fair prediction sets.
Problem
Standard conformal prediction gives only marginal coverage and undercovers underrepresented groups, while group-wise conformal inference achieves group-conditional coverage but yields overly wide prediction sets due to small group sizes.
Approach
Combine clustering of protected groups with similar score distributions (pooling thresholds per cluster) with a surrogate-assisted efficient influence function for the quantile threshold, yielding doubly robust, approximately group-conditional coverage with tighter sets.
Key results
- On the COVE trial, SAGCCI achieves AvgSize 3.61 with CovGap 0.18, versus 3.83/1.09 for SURRO + STANDARD and 3.93/0.14 for SURRO + GROUP.
- In simulations with sigma_S=3, SAGCCI reduces AvgSize by over 60% relative to SURRO + GROUP at N=1000 while increasing CovGap by only 7%.
- Compared with SURRO + STANDARD at N=3000, SAGCCI reduces CovGap by over 80% with similar AvgSize.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SAGCCI instead of SURRO + STANDARD | Conformal prediction on Moderna COVE · Moderna COVE (age-comorbidity groups) | CovGap: 1.09 -> 0.18 | Helped |
| Use SAGCCI instead of SURRO + STANDARD | Conformal prediction on Moderna COVE · Moderna COVE (age-comorbidity groups) | AvgSize: 3.83 -> 3.61 | Helped |
| Replace group-wise calibration with clustered calibration in the surrogate-assisted method | Conformal prediction on Moderna COVE · Moderna COVE (age-comorbidity groups) | AvgSize: 3.93 -> 3.61 | Helped |
| Replace group-wise calibration with clustered calibration in the surrogate-assisted method | Conformal prediction on Moderna COVE · Moderna COVE (age-comorbidity groups) | CovGap: 0.14 -> 0.18 | Mixed |
| Add surrogate outcomes to clustered conformal inference (ablation) | Clustered conformal inference on Moderna COVE · Moderna COVE (age-comorbidity groups) | AvgSize: 4.48 -> 3.61 | Helped |
| Add surrogate outcomes to clustered conformal inference (ablation) | Clustered conformal inference on Moderna COVE · Moderna COVE (age-comorbidity groups) | CovGap: 3.28 -> 0.18 | Helped |
| Add surrogate outcomes to group-wise conformal inference (ablation) | Group-wise conformal inference on Moderna COVE · Moderna COVE (age-comorbidity groups) | AvgSize: 4.63 -> 3.93 | Helped |
| Add surrogate outcomes to group-wise conformal inference (ablation) | Group-wise conformal inference on Moderna COVE · Moderna COVE (age-comorbidity groups) | CovGap: 2.22 -> 0.14 | Helped |
| Use surrogate-assisted clustering instead of surrogate-assisted standard conformal inference | Conformal prediction on Moderna COVE · Moderna COVE (age-comorbidity groups) | Coverage: (0.95, 0.93, 0.96) -> (0.95, 0.95, 0.95) | Helped |
| Increase surrogate predictiveness in SAGCCI | SAGCCI · Simulations | AvgSize | Helped |
| Increase sample size when using SAGCCI | SAGCCI · Simulations | CovGap | Helped |
| Use surrogate-assisted standard conformal inference without accounting for protected groups | Conformal prediction · Simulations | CovGap | Hurt |
Surprising findings
- WCQR with surrogates yields narrower sets than the non-surrogate clustered method but fails to maintain group-conditional coverage, with CovGap not decreasing with sample size.
Limitations
- Coverage guarantee is approximate (up to o(1) and clustering error epsilon), not exact.
- Relies on MAR assumption and overlap/convergence conditions for nuisance models.
- Number of clusters K must be pre-specified with only a heuristic for selection.
Experimental setup
Datasets: Simulated data Moderna COVE COVID-19 vaccine phase 3 trial data
Benchmarks: Simulated data (N=1000-10000) Moderna COVE phase 3 trial
Metrics: AvgSize CovGap group-conditional coverage width
Baselines: NOSURRO + CLUSTER SURRO + GROUP SURRO + STANDARD NOSURRO + STANDARD NOSURRO + GROUP WCQR CFQR
Builds on: Clustered conformal inference (Ding et al., 2024) Weighted conformal quantile regression (Lei & Candès, 2021) Group-conditional conformal (Vovk, 2012) Localized debiased machine learning (Kallus et al., 2024) Conformalized quantile regression (Romano et al., 2019)
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- Self-Organized Conformal Prediction: Reducing Regional Coverage Gaps with Unsupervised Group Discovery (NeurIPS 2026 · similarity 0.85)
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