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This research introduces spectral adaptive conformal prediction, a method designed to maintain reliable uncertainty quantification for time-indexed datasets exhibiting structured non-exchangeability such as seasonal patterns or shifting frequencies. By leveraging local spectral similarity and online updates, the approach dynamically adjusts calibration residuals to correct long-run miss rates in evolving environments where traditional exchangeable assumptions fail. The study validates these improvements through simulations of recurring regimes and real-world U.S. data examples, highlighting the necessity of monitoring effective sample size diagnostics for robust performance.
Spectral Adaptive Conformal Prediction for Structured Non-Exchangeable Data
arXiv:2606.15950v1 Announce Type: cross Abstract: Conformal prediction gives prediction intervals with finite-sample coverage when the data are exchangeable. Many time-indexed datasets are not exchangeable. They have seasons, recurring regimes, changing frequencies, or other forms of structured dependence. This paper studies a simple way to use that structure. We propose spectral adaptive conformal prediction, a method that forms weighted conformal quantiles using local spectral similarity and then updates the target miscoverage level online. The spectral weights choose calibration residuals that look relevant to the current test point. The adaptive update corrects the long-run miss rate when uncertainty changes over time. We give an approximate coverage result for the fixed spectral weighted quantile and a deterministic long-run calibration result for the adaptive update. Simulations with recurring regimes and slowly changing frequencies, together with three U.S. real-data examples, show that the hybrid method can improve on fixed spectral weighting, while also showing that spectral weighting must be monitored through effective sample size diagnostics.
Abstract:Conformal prediction gives prediction intervals with finite-sample coverage when the data are exchangeable. Many time-indexed datasets are not exchangeable. They have seasons, recurring regimes, changing frequencies, or other forms of structured dependence. This paper studies a simple way to use that structure. We propose spectral adaptive conformal prediction, a method that forms weighted conformal quantiles using local spectral similarity and then updates the target miscoverage level online. The spectral weights choose calibration residuals that look relevant to the current test point. The adaptive update corrects the long-run miss rate when uncertainty changes over time. We give an approximate coverage result for the fixed spectral weighted quantile and a deterministic long-run calibration result for the adaptive update. Simulations with recurring regimes and slowly changing frequencies, together with three U.S. real-data examples, show that the hybrid method can improve on fixed spectral weighting, while also showing that spectral weighting must be monitored through effective sample size diagnostics.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2606.15950 [stat.ML]
(or arXiv:2606.15950v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2606.15950 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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