# Network Inference via the Time-Varying Graphical Lasso

arXiv: https://arxiv.org/abs/1703.01958 · HTML: https://mlsanity.com/paper/1703.01958/

## Key facts

- Cited by 55 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Mar 2017.

## Built on by (most cited first, 30 of 55)

- [Learning Time-Varying Graphs from Online Data](https://mlsanity.com/paper/2110.11017/) (2021)
- [Joint Network Topology Inference via a Shared Graphon Model](https://mlsanity.com/paper/2209.08223/) (2022)
- [Joint Gaussian Graphical Model Estimation: A Survey](https://mlsanity.com/paper/2110.10281/) (2021)
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- [Dynamic Multi-Network Mining of Tensor Time Series](https://mlsanity.com/paper/2402.11773/) (2024)
- [Methods for Recovering Conditional Independence Graphs: A Survey](https://mlsanity.com/paper/2211.06829/) (2022)
- [uGLAD: Sparse graph recovery by optimizing deep unrolled networks](https://mlsanity.com/paper/2205.11610/) (2022)
- [Discover governing differential equations from evolving systems](https://mlsanity.com/paper/2301.07863/) (2023)
- [Mining of Switching Sparse Networks for Missing Value Imputation in Multivariate Time Series](https://mlsanity.com/paper/2409.09930/) (2024)
- [Neural Graph Revealers](https://mlsanity.com/paper/2302.13582/) (2023)
- [Inferring Dynamic Networks from Marginals with Iterative Proportional Fitting](https://mlsanity.com/paper/2402.18697/) (2024)
- [Graph Coding for Model Selection and Anomaly Detection in Gaussian Graphical Models](https://mlsanity.com/paper/2102.02431/) (2021)
- [Scalable Inference of Sparsely-changing Markov Random Fields with Strong Statistical Guarantees](https://mlsanity.com/paper/2102.03585/) (2021)
- [Learning Sparse Graph with Minimax Concave Penalty under Gaussian Markov Random Fields](https://mlsanity.com/paper/2109.08666/) (2021)
- [Modeling Regime Shifts in Multiple Time Series](https://mlsanity.com/paper/2109.09692/) (2021)
- [Scalable network reconstruction in subquadratic time](https://mlsanity.com/paper/2401.01404/) (2024)
- [Decentralized Smoothing ADMM for Quantile Regression with Non-Convex Sparse Penalties](https://mlsanity.com/paper/2408.01307/) (2024)
- [Online Learning Of Expanding Graphs](https://mlsanity.com/paper/2409.08660/) (2024)
- [High-Dimensional Differential Parameter Inference in Exponential Family using Time Score Matching](https://mlsanity.com/paper/2410.10637/) (2024)
- [Time-Varying Graph Learning for Data with Heavy-Tailed Distribution](https://mlsanity.com/paper/2501.00606/) (2024)
- [Coarse-to-Fine Learning of Dynamic Causal Structures](https://mlsanity.com/paper/2602.22532/) (2026)
- [Gaussian Experts Selection using Graphical Models](https://mlsanity.com/paper/2102.01496/) (2021)
- [Joint Network Topology Inference via Structured Fusion Regularization](https://mlsanity.com/paper/2103.03471/) (2021)
- [Joint Estimation and Inference for Multi-Experiment Networks of High-Dimensional Point Processes](https://mlsanity.com/paper/2109.11634/) (2021)
- [Time-varying Graph Learning Under Structured Temporal Priors](https://mlsanity.com/paper/2110.05018/) (2021)
- [Efficient Inference of Spatially-varying Gaussian Markov Random Fields with Applications in Gene Regulatory Networks](https://mlsanity.com/paper/2206.10174/) (2022)
- [Online Inference for Mixture Model of Streaming Graph Signals with Non-White Excitation](https://mlsanity.com/paper/2207.14019/) (2022)
- [Solution Path of Time-varying Markov Random Fields with Discrete Regularization](https://mlsanity.com/paper/2307.13750/) (2023)
- [Compressive Recovery of Sparse Precision Matrices](https://mlsanity.com/paper/2311.04673/) (2023)

## Abstract (arXiv)

Many important problems can be modeled as a system of interconnected entities, where each entity is recording time-dependent observations or measurements. In order to spot trends, detect anomalies, and interpret the temporal dynamics of such data, it is essential to understand the relationships between the different entities and how these relationships evolve over time. In this paper, we introduce the time-varying graphical lasso (TVGL), a method of inferring time-varying networks from raw time series data. We cast the problem in terms of estimating a sparse time-varying inverse covariance matrix, which reveals a dynamic network of interdependencies between the entities. Since dynamic network inference is a computationally expensive task, we derive a scalable message-passing algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve this problem in an efficient way. We also discuss several extensions, including a streaming algorithm to update the model and incorporate new observations in real time. Finally, we evaluate our TVGL algorithm on both real and synthetic datasets, obtaining interpretable results and outperforming state-of-the-art baselines in terms of both accuracy and scalability.