Conformal Prediction via Transported Beta Laws
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918510200881152 |
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| author | Ramos, Thiago R. Graziadei, Helton Cabezas, Luben M. C. |
| author_facet | Ramos, Thiago R. Graziadei, Helton Cabezas, Luben M. C. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_19024 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Conformal Prediction via Transported Beta Laws Ramos, Thiago R. Graziadei, Helton Cabezas, Luben M. C. Machine Learning Methodology 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. |
| title | Conformal Prediction via Transported Beta Laws |
| topic | Machine Learning Methodology |
| url | https://arxiv.org/abs/2605.19024 |