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

arXiv: https://arxiv.org/abs/2602.08197 · HTML: https://mlsanity.com/paper/2602.08197/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 49 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Builds on (most cited first, 14 of 14)

- [Network Inference via the Time-Varying Graphical Lasso](https://mlsanity.com/paper/1703.01958/) (2017)
- [Node-Based Learning of Multiple Gaussian Graphical Models](https://mlsanity.com/paper/1303.5145/) (2013)
- [SPARTan: Scalable PARAFAC2 for Large & Sparse Data](https://mlsanity.com/paper/1703.04219/) (2017)
- [Estimating Time-varying Brain Connectivity Networks from Functional MRI Time Series](https://mlsanity.com/paper/1310.3863/) (2013)
- [SSMF: Shifting Seasonal Matrix Factorization](https://mlsanity.com/paper/2110.12763/) (2021)
- [Estimating Time-Varying Graphical Models](https://mlsanity.com/paper/1804.03811/) (2018)
- [Dynamic Multi-Network Mining of Tensor Time Series](https://mlsanity.com/paper/2402.11773/) (2024)
- [Time-dependent spatially varying graphical models, with application to brain fMRI data analysis](https://mlsanity.com/paper/1711.03701/) (2017)
- [Fast and Multi-aspect Mining of Complex Time-stamped Event Streams](https://mlsanity.com/paper/2303.03789/) (2023)
- [Latent Variable Time-varying Network Inference](https://mlsanity.com/paper/1802.03987/) (2018)
- [SliceNStitch: Continuous CP Decomposition of Sparse Tensor Streams](https://mlsanity.com/paper/2102.11517/) (2021)
- [DPar2: Fast and Scalable PARAFAC2 Decomposition for Irregular Dense Tensors](https://mlsanity.com/paper/2203.12798/) (2022)
- [D-Tracker: Modeling Interest Diffusion in Social Activity Tensor Data Streams](https://mlsanity.com/paper/2505.00242/) (2025)
- [Mining Reaction and Diffusion Dynamics in Social Activities](https://mlsanity.com/paper/2208.04846/) (2022)

## Abstract (arXiv)

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.