Spatiotemporal Kronecker Covariance Neural Networks

Abstract: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.

Machine Learning (cs.LG)

arXiv:2609.25326 [cs.LG]

(or arXiv:2609.25326v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.25326 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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