用当前预测样本云动态建模多变量置信椭球，提升预测覆盖率。
SPACE: Sample-cloud Predictive Adaptive Conformal Ellipsoids for Multivariate Time-Series Forecasting
- 基于当前预测样本云直接估计局部协方差结构，避免依赖历史残差。
- 通过动态后向窗口选择校准椭球半径，实现覆盖率达标。
- 适用于多变量时间序列，尤其在分布漂移下表现更稳定。
现代概率时间序列预测器通常通过预测样本表达不确定性。尽管常使用经验分位数转换为名义预测区域，但这些区域缺乏形式化覆盖保证，且在分布漂移下常偏离目标。现有多变量合取方法可在线校准区域，但通常依赖历史残差的固定或累积回看窗口估计几何结构。这种对过去的依赖限制了其利用当前预测瞬时依赖关系的能力，并易受陈旧状态污染。为此，我们提出SPACE，一种针对样本生成型多变量预测器的合取封装器。SPACE通过直接从当前预测样本云估计时间局部协方差几何结构，构建椭球形联合预测区域，并通过动态后向窗口选择方案校准区域半径。在多种多变量数据集、概率预测器及合取基线中，SPACE始终使实际联合与滚动覆盖率更接近名义目标，相较竞争封装器实现更优的覆盖-效率权衡。
原文摘要 · Abstract (English)
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.
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