SPACE：用于多变量时间序列预测的样本云预测自适应共形椭球
SPACE: Sample-cloud Predictive Adaptive Conformal Ellipsoids for Multivariate Time-Series Forecasting
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- Asian Institute of Digital Finance, National University of Singapore（新加坡国立大学亚洲数字金融研究院）
- National University of Singapore（新加坡国立大学）
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中文总结 AI 辅助
针对现有多变量共形预测方法易受陈旧状态污染的问题，提出共形包装器SPACE，通过当前预测样本云估计协方差几何并动态选回溯窗口校准区域，提升了预测覆盖的准确性与效率。
中文摘要 AI 辅助
现代概率时间序列预测器通常通过预测样本来表达不确定性，这些样本虽常通过经验分位数转换为名义预测区域，但模型隐含的集合缺乏正式覆盖保证，且在分布偏移下常偏离名义目标。现有多变量共形方法可在线校准这些区域，但通常使用固定或累积回溯窗口从历史残差估计几何结构，对过去的依赖限制了其利用当前预测瞬时依赖结构的能力，且易受陈旧状态污染。为解决该问题，我们提出SPACE，一种用于生成样本的多变量预测器的共形包装器，它通过直接从当前预测样本云估计时间局部协方差几何来构建椭球联合预测区域，并通过动态回溯窗口选择方案校准区域半径。在各类多变量数据集、概率预测器及共形基线中，SPACE始终使实现的联合覆盖和滚动覆盖更接近名义目标，相对于竞争包装器实现了更优的覆盖-效率权衡。
英文摘要
Modern probabilistic time-series forecasters often express uncertainty through forecast samples. While typically converted into nominal prediction regions using empirical quantiles, these model-implied sets lack formal coverage guarantees and frequently deviate from nominal targets under distribution shift. Existing multivariate conformal methods can calibrate these regions online, but they typically estimate geometry from historical residuals using fixed or accumulating look-back windows. This reliance on the past limits their ability to exploit the instantaneous dependence structure of current predictions and leaves them vulnerable to stale-regime contamination. To address this, we propose SPACE, a conformal wrapper for sample-generating multivariate forecasters. SPACE constructs ellipsoidal joint prediction regions by estimating time-local covariance geometry directly from the current forecast sample cloud, calibrating the region's radius via a dynamic backward window-selection scheme. Across diverse multivariate datasets, probabilistic forecasters, and conformal baselines, SPACE consistently brings realized joint and rolling coverage closer to the nominal target, achieving superior coverage-efficiency tradeoffs relative to competing wrappers.
