Network Inference via the Time-Varying Graphical Lasso

TL;DR

The paper introduces the time-varying graphical lasso (TVGL), a scalable method for inferring dynamic networks from time series data by estimating sparse, evolving inverse covariance matrices, with applications demonstrated on real and synthetic datasets.

Contribution

We develop a scalable message-passing algorithm based on ADMM for efficient inference of time-varying networks, including extensions for real-time updates.

Findings

TVGL outperforms state-of-the-art methods in accuracy

The algorithm is scalable to large datasets

It effectively captures evolving network structures

Abstract

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.