Network Inference via the Time-Varying Graphical Lasso

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.

Query-Specific Knowledge Summarization with Entity Evolutionary Networks

“…In terms of the computation e ciency, in S E , we rst compute S f (t) using equation (6), and then compute Θ(t) for each t using the state-of-the-art Graphical Lasso algorithm [3]. e computation complexity is thus exactly same as the state-of-the-art evolutionary network inference algorithms [5,16].…”

“…Data Generation. Following Hallac et al [5], we generate two evolutionary networks of sizes 20 and 100 and then randomly generate the ground-truth covariance and sample discrete observations over 100 timestamps, where the global and local evolutions occur at time t = 50. At each t, we generate 10 independent samples from the true distribution, with maximum variable value set to 10.…”

“…Compared Algorithms. We compare S E to two baselines: 1) Static [10], which applies the nonparanormal transformation for discrete observations, but aggregate observations from all timestamps to infer a single static network without evolutions, and 2) TVGL [5], which leverages graphical lasso for evolutionary network construction but does not consider discrete observations. Performance Evaluations.…”

Time-varying Graph Learning Based on Sparseness of Temporal Variation

“…However, in many applications where the observations are obtained over a period of time, a time-varying graph will provide a better model. Examples of such applications include estimation of the time-varying brain functional connectivity from EEG or fMRI data [26], identification of temporal transit of biological networks such as protein, RNA, and DNA [27], and inference of relationships among companies from historical stock price data [28], dynamic point cloud processing, and analysis of physical measurement data such as temperature. A straightforward approach to estimate a time-varying graph would consist of aggregating temporal observations into nonoverlapping windows and then using an existing static graph learning method to estimate a graph for each time windows.…”

A Novel Graphical Lasso Based Approach Towards Segmentation Analysis in Energy Game-Theoretic Frameworks

“…Historically, Graphical Lasso has been used in various fields of science, ranging from study of how individual elements of the cell interact with each other [9] and to the broad area of computer vision for scene labelling [10]. A modified version of the original algorithm, named time-varying graphical lasso, has been used on financial and automotive data [20]. However, the novelties of graphical lasso has not been well utilized in the area of energy cyber-physical systems.…”