Interpretable Dynamic Network Modeling of Tensor Time Series via Kronecker Time-Varying Graphical Lasso

2026-02-09

AI Summary

Modeling dynamic dependencies among variables in high-dimensional tensor time series is challenged by complex network structures, poor interpretability, and high computational costs. This work proposes the Kronecker Time-Varying Graph Lasso, which leverages the Kronecker product to model dynamic networks for each mode separately, thereby avoiding entanglement across modes. This approach enhances interpretability while substantially reducing computational complexity. Notably, the method supports streaming computation, rendering its complexity independent of the sequence length. Experimental results demonstrate that the proposed method achieves higher accuracy in edge estimation and faster computation than existing approaches on synthetic data, and further validates its practical utility on real-world datasets.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Web Mining and Content Analysis: Models for Web evolution

Abstract

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.

Problem

• tensor time series
• dynamic network
• time-varying dependencies
• interpretable modeling
• Kronecker product

Innovation

• Kronecker product
• time-varying graphical model
• tensor time series
• interpretable dynamic network
• streaming algorithm