Standard CP
One ball around the mixture mean
—Held-out coverage
—Mean set size
ORCA · Project page
Generative Conformal Prediction with Optimized Coverage Allocation
Accepted to NeurIPS 2026
ORCA: Optimized Ranking and Coverage Allocation. Generated samples are ranked by a local density proxy. ORCA allocates different radii across those ranks, then calibrates their common scale for finite-sample marginal coverage.
The linked preprint and preliminary code use the earlier vectorized-score / PCP-VCR title. An updated paper version is forthcoming.
Why allocate coverage?
PCP places equal-radius balls around generated samples. A single radius can spend substantial volume on rare, diffuse regions. ORCA learns rank-specific radii on an exploration split, allowing a compact set around the dominant mass while a separate calibration split maintains marginal coverage.
01 Explore
Draw conditional samples and rank each draw by average distance to its four nearest neighbors.
02 Optimize
Use exploration responses to allocate radii by rank, minimizing a sum-of-ball-volumes proxy under an empirical coverage constraint.
03 Calibrate
On an independent calibration split, find one multiplier for the learned radius vector.
Standard CP, PCP, and ORCA
Compare three calibrated set geometries on the same generated samples and response distribution.
What changes when you click? The 1D/2D and Experiment buttons load results computed offline. The radius-allocation MILP and independent test evaluation do not rerun in your browser. Clicking a plot only moves the response probe.
Saved experiment
90% target300 explore · 1,000 calibrate
1,000 independent test cases
1,000 independent test cases
PCP
Equal-radius balls around generated samples
—Held-out coverage
—Mean set size
ORCA
Rank-specific radii, calibrated together
—Held-out coverage
—Mean set size
True density (contrast enhanced)Generated point / CP meanMixture center + 1σ contour+Shared response probe
Held-out coverage uses 1,000 test responses. Mean set size uses 250 independent test draws; the plotted set is one separate illustration. Plot colors make low-density components visible without changing the set geometry or reported measurements. The three displayed experiments are selected examples where ORCA's measured mean set size is smaller than PCP's; they are not an overall performance estimate.
Data generation, calibration, and selection
Data generation. For each response, draw 30 independent generated points from the same Gaussian mixture. Rank them by mean distance to their four nearest generated neighbors. The fixed-input generator is correctly specified. One-dimensional union length is exact; two-dimensional union area is estimated on a 100×100 grid around each set.
Optimization. Select rank-specific radii from 15 exploration-distance candidates per rank using a binary MILP with a 2% relative solver gap. The objective Σᵣ Qᵣᵈ is a sum-of-ball-volumes proxy, not exact union volume. This is an offline discretized illustration, not the paper's full-candidate MILP benchmark.
Calibration. Standard CP uses distance from the mixture mean. PCP uses distance to the nearest generated point. ORCA uses the smallest rank-normalized distance. Each method uses the ⌈(n + 1)(1 − α)⌉-th calibration score for 90% marginal coverage. Calibration and test sets are independent of the exploration data.
Selection and scope. The 60/20/20 mixtures we tested did not generally improve ORCA set size at a 90% target. The displayed 1D distribution has weights 60/32/8; the displayed 2D distribution has weights 92/8, with the diffuse mode moved closer and made narrower. The page shows three selected positive runs per dimension. The downloadable results include all six screened runs per dimension, including ties and unfavorable outcomes. These examples show the mechanism, not a general efficiency claim.
Coverage. Split-conformal validity requires exchangeable calibration and test instances and an allocation chosen independently of calibration. A finite test percentage can fall below 90%.
| Experiment | CP cov. | PCP cov. | ORCA cov. | CP size | PCP size | ORCA size |
|---|
Cite the current arXiv version
Minxing Zheng and Shixiang Zhu. “Generative Conformal Prediction with Vectorized Non-Conformity Scores.” arXiv:2410.13735, 2024.
This is the title and year of the version currently on arXiv. The citation can be updated when the revised paper and proceedings are available.