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Generative Conformal Prediction with Optimized Coverage Allocation

NeurIPS 2026 · Learning theory and algorithms › Prediction and decision losses · approach: Conformal prediction sets

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Proposes ORCA, a three-stage generative conformal prediction method that ranks generated samples by averaged m-NN density, allocates rank-dependent coverage radii via a MILP-based optimization, and calibrates with split conformal to obtain smaller valid uncertainty sets.

Problem

Conformal prediction often yields overly conservative uncertainty sets when the conditional distribution is multimodal or heterogeneous, due to limited model expressiveness and simplistic nonconformity scores.

Approach

Use samples from a generative model, rank them by local density (averaged m-NN distance), keep a full rank-dependent distance vector instead of a scalar score, and choose per-rank radii by solving a volume-minimizing coverage allocation problem (exact MILP, with LP and greedy approximations) before split-conformal calibration.

Key results

• On synthetic datasets, ORCA attains the smallest or near-smallest efficiency on nearly all six datasets (e.g., S-shape Eff 0.51 vs PCP 0.58) while keeping marginal coverage near 0.90.
• On MNIST, ORCA achieves a lower off-class rate than PCP (0.16 vs 0.22) with K=40.
• On real datasets, ORCA gives the smallest sets on Fb1 (Eff 3.70 vs PCP 7.79) with coverage close to nominal across 30 runs.

Surprising findings

• Worst-slab conditional coverage of ORCA is sometimes lower than PCP or R2CCP on real datasets (e.g., Fb1 0.80 vs PCP 0.82), indicating efficiency gains can cost conditional coverage.

Limitations

• Stage 2 uses an additive volume cost that ignores overlap between rank-dependent balls.
• Exact MILP worst-case runtime is exponential in K*n1; scalability relies on LP or greedy approximations.
• Euclidean metric may be poorly suited to high-dimensional outputs such as images.

Experimental setup

Datasets: Circles Moon S-shape Spiral Roll Mixture Gaussian MNIST Blog Feedback Facebook Comment Volume (Fb1) Facebook Comment Volume (Fb2) MEPS Protein Structure

Benchmarks: Circles Moon S-shape Spiral Roll Mixture Gaussian MNIST Blog Feedback Facebook Comment Volume (Fb1) Facebook Comment Volume (Fb2) MEPS Protein Structure

Metrics: marginal coverage worst-slab conditional coverage prediction set efficiency (average set size) off-class rate

Baselines: CQR CHR DCP DistSplit CDSplit PCP CRD R2CCP

Builds on: Probabilistic Conformal Prediction Conformalized Quantile Regression Conformal Histogram Regression Covariance-weighted conformal prediction

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