Optimal Spatio-Temporal Decoupling for Bayesian Conformal Prediction

arXiv cs.LG / 5/4/2026

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Key Points

The paper addresses limitations in Online Conformal Prediction, where feedback-based methods can under-cover and produce high interval variance during sudden regime shifts, and temporally discounted Bayesian CP can lag structurally and produce miscalibrated interval bloat.
It proposes State-Adaptive Bayesian Conformal Prediction (SA-BCP), which uses a gating mechanism that decouples long-term temporal inertia from spatial kernel-density evidence to proactively adjust interval widths.
The authors provide rigorous proofs of the proposed mechanism’s optimality and characterize a minimax bias–variance tradeoff controlled by an evidence threshold K.
Experiments on volatile financial time series (2016–2026), including AMD, Gold, and GBP/USD, show SA-BCP improves coverage behavior and reduces uncalibrated interval bloat by about 10%–37% for high-confidence settings.
Results indicate SA-BCP consistently minimizes the strictly proper Winkler score across multiple confidence levels, balancing conditional reliability with predictive efficiency.

Abstract

Online Conformal Prediction (CP) struggles to balance temporal adaptability and structural stability. Feedback-driven methods (e.g., Adaptive Conformal Inference (ACI)) suffer from systemic marginal under-coverage and high interval variance during abrupt shifts, while temporally discounted Bayesian CP suffers from severe structural lag and uncalibrated interval bloat. We propose State-Adaptive Bayesian Conformal Prediction (SA-BCP) to achieve optimal spatio-temporal decoupling. By gating long-term temporal inertia with spatial kernel-density evidence, SA-BCP proactively expands intervals for recognized historical regimes while maintaining tight efficiency during stable states. We rigorously prove this mechanism's optimality, identifying a minimax bias-variance tradeoff governed by an evidence threshold

K

. Extensive benchmarks on volatile financial datasets (2016--2026), including AMD, Gold, and GBP/USD, demonstrate that SA-BCP consistently minimizes the strictly proper Winkler score across diverse confidence levels. Specifically, SA-BCP resolves the systematic under-coverage inherent to ACI variants while simultaneously reducing the uncalibrated interval bloat of Bayesian CP by 10\% to 37\% under high-confidence requests. By elegantly navigating this tradeoff, SA-BCP achieves an optimal balance between conditional reliability and predictive efficiency.