Tail allocation for conformal prediction intervals

• URL: http://arxiv.org/abs/2604.25202v1
• Date: Tue, 28 Apr 2026 04:14:27 GMT
• Title: Tail allocation for conformal prediction intervals
• Abstract summary: We study split-conformal prediction for regression when the reported prediction set must be a single interval, at target marginal coverage $1-$, where $$ is the nominal miscoverage level.<n>Under this reporting constraint, the natural conditional target is the shortest interval with conditional mass at least $1-$, rather than an equal-tailed interval or a possibly disconnected high-probability set.<n>We parameterize this single-interval by a lower-tail allocation, which determines how the nominal miscoverage $$ is split between the two endpoints.
• Score: 1.0163716169047106
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study split-conformal prediction for regression when the reported prediction set must be a single interval, at target marginal coverage $1-α$, where $α$ is the nominal miscoverage level. Under this reporting constraint, the natural conditional target is the shortest interval with conditional mass at least $1-α$, rather than an equal-tailed interval or a possibly disconnected high-probability set. We parameterize this single-interval oracle by a lower-tail allocation, which determines how the nominal miscoverage $α$ is split between the two endpoints, and propose tail-allocation conformalized quantile regression (TA-CQR). TA-CQR estimates this allocation by searching over quantile-defined cores and then applies nonnegative additive split-conformal calibration, retaining exact finite-sample marginal coverage under exchangeability. The main contribution is theoretical. We characterize the oracle geometry, including its highest-density interpretation under unimodality and the positive connectedness cost induced by disconnected highest-density sets. We prove local recovery of the selected allocation and core, establish that calibration radii are asymptotically negligible under endpoint-density conditions, and give a finite-sample calibrated length oracle inequality with explicit grid, endpoint-quantile estimation, and calibration-sampling terms. Simulations and real-data examples report coverage and length jointly.

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