Filtered Conformal Ellipsoids for Graph-Native Time Series
图结构时间序列的滤波共形预测椭球AI 解读 ↓
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图结构时间序列的滤波共形预测椭球
- 研究问题
- 如何为具有坐标间依赖的多元时间序列构造联合预测椭球，使其适应预测协方差，并在分数存在依赖时评估覆盖误差？
- 方法与思路
- 作者冻结状态空间滤波器，用预测均值和协方差形成 Mahalanobis 分数，再以分割共形校准半径，并分析输出预测律的收缩。
- 材料陈述的贡献
- 摘要称，在指定稳定性与依赖条件下可得近似覆盖界；高斯预言机可实现时还可比较体积，部分交通基准显示较尖锐椭球。
- 阅读关注点
- 应核对预测律商空间、可观测性条件及依赖包络的定义，并区分基本覆盖界、额外混合条件下的更强界和体积比较。
- 阅读边界
- 这是 arXiv 预印本，同行评审或接收未核实；保证依赖特定条件，且摘要明确指出全图规模及非图数据中其他基线可能更强。
原文摘要
Joint prediction sets for multivariate time series should control a single event while adapting to cross-coordinate dependence. We study filtered conformal ellipsoids: a frozen state-space filter emits a one-step predictive mean and covariance, and split-conformal calibration is applied to the resulting Mahalanobis scores. The filter is used to choose the ellipsoid shape; conformal calibration chooses the scalar radius, so the construction benefits from a learned predictive covariance without relying on Gaussian tail probabilities for coverage. The main difficulty is that filtered scores are dependent and learned recurrent filters need not contract in their raw hidden state; we therefore analyse contraction in an observable predictive-law quotient that identifies hidden states producing the same future sequence of emitted Gaussian laws. Under a stable Bayes Gaussian-projection filter, covariance bounds, and a finite-horizon observability Fisher condition, small excess Gaussian negative log-likelihood implies contraction of the learned emitted laws. Combined with a threshold-autocovariance envelope this yields a Chebyshev-type approximate coverage bound for filtered split-conformal prediction under dependence; a sharper Bernstein-type bound requires an additional geometric-mixing concentration assumption. Under Gaussian oracle realisability we also obtain a near-oracle log-volume comparison within the class of conditionally valid Gaussian ellipsoid rules. We instantiate the framework with a GCN-GRU filter with diagonal-plus-low-rank covariance. On moderate-size graph-native traffic benchmarks (METRLA-$20$ and PEMSBAY-$50$), the learned filter gives sharper at-target ellipsoids than static-covariance and non-filter baselines; at full-graph scale and on non-graph-native datasets, factor and copula baselines can be stronger.