用克罗内克积建模多维时序数据的动态网络,提升可解释性与计算效率。
Interpretable Dynamic Network Modeling of Tensor Time Series via Kronecker Time-Varying Graphical Lasso
- 采用克罗内克积分解各维度动态网络,避免复杂纠缠结构。
- 在合成数据上准确率更高,计算时间显著降低。
- 适合高维时序数据建模,尤其适用于流式处理场景。
随着网络服务的快速发展,金融、医疗和在线平台等领域产生了大量时序数据。这些数据常涉及多个变量间的协同演化,准确估计变量间随时间变化的依赖关系(即动态网络结构)对建模至关重要。然而,现实数据常表现为多维度张量时序,导致网络结构庞大且高度耦合,难以解释且计算成本高昂。本文提出克罗内克时变图模型(KTVGL),通过克罗内克积形式估计各维度的动态网络,避免复杂耦合结构,实现可解释建模。该方法的分块网络结构有效防止计算时间随数据维度呈指数增长,并可扩展为流式算法,使计算时间独立于序列长度。合成数据实验表明,本方法在边缘估计精度上优于现有方法,同时计算更高效。真实数据案例进一步验证其实际价值。源代码与数据集见https://github.com/Higashiguchi-Shingo/KTVGL。
原文摘要 · Abstract (English)
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.
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