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arXiv · 2509.15349

Probabilistic Conformal Coverage Guarantees in Small-Data Settings

Petrus H. Zwart
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Abstract

Conformal prediction provides distribution-free prediction sets with guaranteed marginal coverage. However, in split conformal prediction this guarantee is training-conditional only in expectation: across many calibration draws, the average coverage equals the nominal level, but the realized coverage for a single calibration set may vary substantially. This variance undermines effective risk control in practical applications. Here we introduce the Small Sample Beta Correction (SSBC), a plug-and-play adjustment to the conformal significance level that leverages the exact finite-sample distribution of conformal coverage to provide probabilistic guarantees, ensuring that with user-defined probability over the calibration draw, the deployed predictor achieves at least the desired coverage.

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Petrus H. Zwart. 2025-09-18. Probabilistic Conformal Coverage Guarantees in Small-Data Settings. https://arxiv.org/abs/2509.15349

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