Uncertainty quantification in train delay prediction with conformal prediction.

Authors

Rui Luo, Xiaoyi Su, Khuong An Nguyen

Published in

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences. Volume 384. Issue 2327. Aug 27, 2026.

Abstract

Predicting train delays is crucial for railway operations and passenger experience, but point predictions fail to capture uncertainty, limiting their use in risk-aware decisions. Existing uncertainty quantification (UQ) methods often rely on unverifiable assumptions and produce miscalibrated intervals. This paper evaluates conformal prediction (CP) as a distribution-free framework for generating prediction intervals with rigorous coverage guarantees. Using a large-scale dataset from Southeastern Railway in the UK, we show that UQ methods such as quantile regression (QR), Monte Carlo dropout and deep ensembles (DE) frequently under- or over-cover nominal levels. By contrast, CP corrects miscalibration across models, ensuring valid marginal coverage. Conformalized QR (CQR) achieves the best efficiency by producing adaptively sized intervals while maintaining calibration. To address heterogeneity across stations, we apply Mondrian CP (MCP), which enforces conditional coverage within strata. Empirical results confirm MCP delivers reliable intervals for each subgroup. Our work demonstrates that CP is a model-agnostic, robust framework for trustworthy UQ, offering a practical pathway to reliable risk assessment in transportation and other high-stakes domains. This article is part of the theme issue 'Advancing uncertainty quantification in AI systems'.

PMID:
42656160
Bibliographic data and abstract were imported from PubMed on 27 Aug 2026.

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