提出一种自适应贝叶斯置信预测方法，平衡快速响应与稳定覆盖。
Optimal Spatio-Temporal Decoupling for Bayesian Conformal Prediction
- 用门控凸组合融合长期时序惯性和局部空间证据
- 在紧覆盖率下置信区间锐度提升至原方法的3倍，Winkler得分降低
- 支持在线选择阈值，适用于金融与气象等动态场景
在线共形预测需在快速适应分布变化与保持覆盖稳定性之间权衡：反馈驱动方法反应迅速但波动大，强折扣贝叶斯方法滞后且在紧覆盖率下区间过宽。本文提出状态自适应贝叶斯共形预测（SA-BCP），将预测分位数设为长期时序惯性与基于核密度估计的局部空间证据的门控凸组合，由单个可解释的证据阈值K控制。理论证明：(i) 区间渐近边际有效性，偏差随空间证据积累趋于零（循环状态下精确）；(ii) MSE最优阈值闭式解 $K^*_{\mathrm{MSE}}=α(1-α)/M^{\mathcal{T}}$，权衡覆盖率指示器方差与时序结构偏差 $M^{\mathcal{T}}$；(iii) 提出滚动起源法在线选择K——平稳下一致，$O(\sqrt{T\log N})$ 对最优固定K的遗憾，分段变体在子线性阈值切换次数 $B_T=o(T)$ 下具次线性动态遗憾。在四个金融波动率与天气数据集、三种目标覆盖率、八种基线中，SA-BCP在多数设置下实现名义或以上覆盖，同时显著更锐利区间——在最紧覆盖率下比折扣贝叶斯共形预测的Winkler得分低约3倍。覆盖率匹配审计确认效率提升非因欠覆盖所致。主要局限：一专门化波动率模型在自有数据上仍更高效，但不跨域迁移。
原文摘要 · Abstract (English)
Online conformal prediction must balance fast adaptation to distribution shift against stable coverage: feedback-driven methods react quickly but become volatile, while strongly discounted Bayesian methods lag and inflate intervals at tight coverage. We introduce \textbf{State-Adaptive Bayesian Conformal Prediction (SA-BCP)}, which forms the predictive quantile as a gated convex combination of long-term temporal inertia and local spatial evidence from a kernel density estimate, controlled by a single interpretable evidence threshold $K$. We establish three results: (i) asymptotic marginal validity of the resulting intervals up to a gate-controlled bias that vanishes as spatial evidence accumulates (exact under recurrent states); (ii) a closed-form expression for the MSE-optimal threshold, $K^*_{\mathrm{MSE}}=α(1-α)/M^{\mathcal{T}}$, trading the coverage-indicator (Bernoulli) variance against the temporal structural bias $M^{\mathcal{T}}$; and (iii) a rolling-origin procedure for selecting $K$ online -- consistent under stationarity, with $O(\sqrt{T\log N})$ regret against the best fixed $K$ and, for a segmented variant, a sublinear dynamic-regret bound under sublinearly many ($B_T=o(T)$) threshold shifts. Across four financial-volatility and weather datasets, three target coverage levels, and eight baselines, SA-BCP attains at-or-above-nominal coverage in most settings while producing substantially sharper intervals -- up to roughly $3\times$ lower Winkler score than discounted Bayesian CP at the tightest coverage -- and a coverage-matched audit confirms these efficiency gains are not an artifact of under-coverage. We disclose our principal limitation: a volatility-specialized CF-GARCH competitor remains more efficient on its home volatility-base series, though it does not transfer across domains.
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