🤖 AI Summary
Existing online conformal prediction methods typically support only a single confidence level, making it difficult to simultaneously ensure validity and nested prediction sets across multiple coverage levels, thereby failing to accommodate heterogeneous user risk preferences requiring full-spectrum uncertainty calibration. This work proposes two novel online conformal prediction approaches that, for the first time, incorporate nesting constraints into an online framework. By jointly estimating quantiles at multiple coverage levels and leveraging cross-quantile information sharing, non-crossing constraints, and low-regret online optimization, the proposed methods enable synchronized and efficient uncertainty quantification across the entire risk spectrum. Experiments on both synthetic and real-world data demonstrate that the methods achieve strict nesting, stable empirical coverage, and significantly improved prediction efficiency compared to existing baselines.
📝 Abstract
Conformal prediction provides a principled framework for uncertainty quantification with finite-sample coverage guarantees. While recent work has extended conformal prediction to online and sequential settings, existing methods typically focus on a single coverage level and do not ensure consistency across multiple confidence levels. In many real-world applications, such as weather forecasting, macroeconomic prediction, and risk management, different users operate under heterogeneous risk tolerances and require calibrated uncertainty estimates across a range of coverage levels. In such settings, it is desirable to produce prediction sets corresponding to different coverage levels that are nested and valid simultaneously. In this paper, we propose two novel online conformal prediction methods that output \emph{nested prediction sets} across a range of coverage levels, enabling simultaneous uncertainty quantification across the entire risk spectrum. Beyond interpretability, jointly estimating multiple coverage levels is known to improve statistical efficiency in classical quantile regression by enforcing non-crossing constraints and sharing information across quantiles. Our approaches leverage an online optimization perspective with small regret that translates to quantile estimation error control while enforcing nestedness of prediction sets. Empirical results on synthetic and real-world datasets, including applications in forecasting tasks with heterogeneous risk requirements, demonstrate that our method achieves stable coverage across all levels, strictly nested prediction sets, and improved efficiency compared to existing online conformal baselines.