时空Kronecker协方差神经网络

中文摘要 AI 辅助

多元时间序列包含跨越空间和时间的复杂模式。虽然基于协方差的统计工具如时空主成分分析（ST-PCA）有助于识别这些模式，但它们仅限于线性操作，并且在数据有限时容易出现估计误差。最近的基于协方差的时空神经网络提供了更稳定、非线性的替代方案，但它们忽略了不同时间步之间的相关性。为了解决这个问题，我们引入了Kronecker协方差神经网络（KVNN），一种时间图神经网络，通过Kronecker积的和来表示时空协方差矩阵，其中空间和时间依赖性被解耦。通过对空间和时间分量实施滤波操作，KVNN实现了强大的处理能力，允许严格的谱分析，并且对有限样本估计误差具有可证明的稳定性，最终解决了ST-PCA的所有局限性。我们在五个真实世界数据集上表明，KVNN实现了强大的预测性能，通常需要比竞争方法少得多的可训练参数，并且在估计噪声下保持一致。

英文摘要

Multivariate time series contain complex patterns that span across both space and time. While covariance-based statistical tools like spatiotemporal Principal Component Analysis (ST-PCA) help identify these patterns, they are limited to linear operations and prone to estimation errors with limited data. Recent covariance-based spatiotemporal neural networks offer more stable, non-linear alternatives, but they ignore correlations across different time steps. To solve this, we introduce the Kronecker coVariance Neural Network (KVNN), a temporal graph neural network that represents the spatiotemporal covariance matrix via a sum of Kronecker products where spatial and temporal dependencies are decoupled. By implementing filtering operations on spatial and temporal components, KVNNs achieve expressive processing capabilities, admit a rigorous spectral analysis, and are provably stable to finite-sample estimation errors, ultimately addressing all of ST-PCA's limitations. We show on five real-world datasets that KVNNs achieve strong forecasting performance, often requiring significantly fewer trainable parameters than competitive methods, and are consistent under estimation noise.

发表机构

• Delft University of Technology（代尔夫特理工大学）

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