Online Conformal Prediction for Non-Exchangeable Panel Data

2026-05-17

AI Summary

This work addresses the challenge that temporal dependence and cross-sectional heterogeneity in panel data violate the exchangeability assumption required by conformal prediction, leading to unreliable uncertainty quantification. To overcome this, the authors propose an online conformal prediction framework tailored for non-exchangeable panel data, featuring two key innovations: first, constructing calibration sets by weighting contemporaneous units based on historical similarity; second, adaptively adjusting miscoverage levels using sparse feedback. The method is distribution-free, compatible with any base predictive model, and demonstrably improves worst-case unit coverage on both synthetic and real-world datasets. By adaptively allocating prediction interval widths, it achieves more efficient and balanced uncertainty quantification across heterogeneous units.

Abstract

Panel data, in which multiple units are repeatedly observed over time, arise throughout science and engineering. Quantifying predictive uncertainty in such settings is challenging because conformal prediction, while distribution-free and model-agnostic, classically relies on exchangeability assumptions that fail under temporal dependence and unit heterogeneity. We propose a simple online conformal framework for non-exchangeable panel data. The method exploits a key feature of online panel prediction: when a forecast is required for one unit, contemporaneous outcomes from related units may already be observed and can serve as a calibration panel. At each round, prediction sets are formed using currently observed calibration units together with two adaptive quantities: history-based similarity weights that emphasize calibration units resembling the target, and an adaptive miscoverage level that is updated whenever target feedback is revealed. This two-state design yields a stepwise coverage bound and a long-run coverage guarantee. Empirically, across synthetic and real panel data sets, the method improves coverage on the worst-covered target units through adaptive interval-width allocation rather than uniform inflation. The two states are complementary: similarity weights protect coverage when target feedback is sparse, while the adaptive level further improves coverage as feedback accumulates.

Problem

• conformal prediction
• panel data
• non-exchangeability
• predictive uncertainty
• temporal dependence

Innovation

• online conformal prediction
• non-exchangeable panel data
• adaptive calibration
• similarity weighting
• coverage guarantee