With the rapid development of web services, large amounts of time series data are generated and accumulated across various domains such as finance, healthcare, and online platforms. As such data often co-evolves with multiple variables interacting with each other, estimating the time-varying dependencies between variables (i.e., the dynamic network structure) has become crucial for accurate modeling. However, real-world data is often represented as tensor time series with multiple modes, resulting in large, entangled networks that are hard to interpret and computationally intensive to estimate. In this paper, we propose Kronecker Time-Varying Graphical Lasso (KTVGL), a method designed for modeling tensor time series. Our approach estimates mode-specific dynamic networks in a Kronecker product form, thereby avoiding overly complex entangled structures and producing interpretable modeling results. Moreover, the partitioned network structure prevents the exponential growth of computational time with data dimension. In addition, our method can be extended to stream algorithms, making the computational time independent of the sequence length. Experiments on synthetic data show that the proposed method achieves higher edge estimation accuracy than existing methods while requiring less computation time. To further demonstrate its practical value, we also present a case study using real-world data. Our source code and datasets are available at https://github.com/Higashiguchi-Shingo/KTVGL.

翻译：随着网络服务的快速发展，金融、医疗和在线平台等各个领域产生并积累了大量的时间序列数据。由于此类数据通常伴随着多个相互作用的变量共同演化，估计变量间的时变依赖关系（即动态网络结构）已成为精确建模的关键。然而，现实世界中的数据常以多模态的张量时间序列形式呈现，导致网络结构庞大且相互纠缠，难以解释且计算成本高昂。本文提出Kronecker时变图套索（KTVGL），一种专为张量时间序列建模设计的方法。我们的方法以Kronecker积形式估计各模态的动态网络，从而避免过度复杂的纠缠结构，并产生可解释的建模结果。此外，分块网络结构防止了计算时间随数据维度呈指数增长。同时，我们的方法可扩展为流式算法，使计算时间与序列长度无关。在合成数据上的实验表明，所提方法在减少计算时间的同时，比现有方法实现了更高的边估计精度。为进一步证明其实际价值，我们还提供了基于真实数据的案例研究。源代码与数据集可在https://github.com/Higashiguchi-Shingo/KTVGL获取。