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Co-optimization for Adaptive Conformal Prediction

NeurIPS 2026 · Learning theory and algorithms › Prediction and decision losses · approach: Conformal prediction sets · 0 citations (OpenAlex)

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Proposes CoCP, which alternately learns a radius via folded pinball-loss quantile regression and a center via a sigmoid soft-coverage loss, then applies split-conformal calibration, claiming asymptotic recovery of the HDI length.

Problem

Standard conformal regression intervals such as CQR use fixed, equal-tailed centers, which yields inefficiently long intervals under heteroscedasticity and skewness.

Approach

Jointly learns a center m(x) and radius h(x): the radius tracks the folded (1-alpha) residual quantile via pinball loss, while the center is refined by maximizing a sigmoid soft-coverage objective whose gradients concentrate at the interval boundaries, followed by normalized split-conformal calibration.

Key results

• On synthetic LogNormal, CoCP reduces length from 1.1110 (CQR) to 0.9621, close to the Oracle 0.9591, and ConMAE 0.0064 vs 0.0122.
• On Exponential, CoCP length 1.1351 vs CQR 1.4222 (about 20% shorter) with ConMAE 0.0069 vs 0.0172.
• On real data CoCP has shortest length on 5 of 7 datasets; on blog and facebook-2 CHR is shorter (2.5531 and 1.4582 vs CoCP 2.7080 and 1.5156).

Surprising findings

• CHR yields shorter real-data intervals than CoCP on blog and facebook-2, so CoCP is not uniformly most efficient.

Limitations

• Theory relies on strong assumptions (unimodality, density bounds, consistency rates) and only asymptotic results.
• Restricted to one-dimensional responses; multivariate extension left open.
• Not uniformly best on real data: CHR shorter on blog and facebook-2.

Experimental setup

Datasets: synthetic Normal, Exponential, LogNormal bike bio blog facebook-1 facebook-2 homes supercon.

Benchmarks: synthetic Normal synthetic LogNormal synthetic Exponential bike bio blog facebook-1 facebook-2 homes supercon.

Metrics: coverage length ConMAE MSCE WSC l1-ERT l2-ERT

Baselines: Split CQR CPL Naive CC CPCP RCP C-HDR CHR

Builds on: conformalized quantile regression split conformal prediction conformal histogram regression colorful pinball conformal prediction

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