Conformal Prediction via Transported Beta Laws

• URL: http://arxiv.org/abs/2605.19024v1
• Date: Mon, 18 May 2026 18:46:39 GMT
• Title: Conformal Prediction via Transported Beta Laws
• Abstract summary: We study the law of the calibration-conditional coverage induced by a realized conformal threshold.<n>We take this beta law as a finite-sample reference object and quantify departures from it using Wasserstein distances.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Split conformal prediction provides finite-sample marginal coverage under exchangeability, but this guarantee averages over the random calibration sample. We study instead the law of the calibration-conditional coverage induced by a realized conformal threshold. In the continuous i.i.d. setting this law is exactly $Beta(k,n+1-k)$, so the usual marginal guarantee corresponds to its mean. We take this beta law as a finite-sample reference object and quantify departures from it using Wasserstein distances on $[0,1]$. The framework yields direct bounds on marginal coverage gaps and on bad-calibration probabilities, and separates different sources of non-i.i.d. behavior according to how they deform the beta reference: test-side shift acts through a transport map on the coverage scale, while calibration dependence changes the order-statistic law itself. We instantiate the framework in scale-shift, clustered, and stationary mixing settings, where the induced deformations can be characterized explicitly or through Berry-Esseen approximations. Simulations on dependent processes confirm that the first-order approximation tracks the empirical Wasserstein distance even at moderate sample sizes.

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