模型无关的在线证书驱动校准用于分布漂移下的时间序列预测
Model-Agnostic Online Certificate-Driven Calibration for Time Series Forecasting Under Distribution Shift
AI总结：
提出模型无关的在线鞅概率近似正确贝叶斯框架，利用证书作为正则化器校准预测器，在分布漂移下提升时间序列预测的稳定性和准确性。
AI中文摘要：
时间序列的分布外泛化要求预测器在部署动态与训练条件不同时（由于协变量漂移、概念漂移和时间依赖性）保持可靠。概率近似正确贝叶斯域自适应通过将目标风险分解为源风险项、源到目标失配项和复杂度项来提供可计算的证书，但标准分析依赖于独立采样和分布稳定性，这些假设在时间序列中因序列依赖和非平稳漂移而被违反。我们提出了一种模型无关的在线鞅概率近似正确贝叶斯框架，该框架在时间依赖和分布漂移下产生有限样本证书。该证书用鞅集中替代独立样本集中，以适应损失规模和可预测变化。我们使用该证书作为在线校准的替代正则化器，通过在固定的预测骨干之上训练一个门控残差贝叶斯头，产生一个校正更新，当门关闭时恢复到骨干预测。在线校准结合了源风险锚、后验漂移惩罚和从预测前观察到的目标窗口计算的时间自适应失配项。它遵循先预测后更新的协议，其中结果仅在预测后可用，并用于更新后续预测。在卷积、基于注意力和基于大语言模型的预测器上的实验表明，在协变量和概念漂移下，稳定性和准确性均有所提高。
英文摘要：
Time series out-of-distribution generalization requires forecasters to remain reliable when deployment dynamics differ from training conditions due to covariate shift, concept shift, and temporal dependence. Probably Approximately Correct Bayesian domain adaptation provides computable certificates by decomposing target risk into a source risk term, a source-to-target mismatch term, and a complexity term, but standard analyses rely on independent sampling and distributional stability, assumptions that are violated in time series by serial dependence and nonstationary shift. We propose a model-agnostic online martingale Probably Approximately Correct Bayesian framework that yields finite-sample certificates under temporal dependence and distribution shift. The certificate replaces independent-sample concentration with martingale concentration that adapts to loss scale and predictable variation. We use the certificate as a surrogate regularizer for online calibration by training a gated residual Bayesian head on top of a fixed forecasting backbone, producing a corrective update that reverts to the backbone prediction when the gate is closed. Online calibration combines a source risk anchor, a posterior-shift penalty, and a time-adaptive mismatch term computed from target windows observed before forecasting. It follows a predict-then-update protocol in which outcomes become available only after forecasting and are used to update subsequent predictions. Experiments across convolutional, attention-based, and large language model-based forecasters show improved stability and accuracy under covariate and concept shift.
