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Many important problems can be modeled as a system of interconnectedentities, where each entity is recording time-dependent observations ormeasurements. In order to spot trends, detect anomalies, and interpret thetemporal dynamics of such data, it is essential to understand the relationshipsbetween the different entities and how these relationships evolve over time. Inthis paper, we introduce the time-varying graphical lasso (TVGL), a method ofinferring time-varying networks from raw time series data. We cast the problemin terms of estimating a sparse time-varying inverse covariance matrix, whichreveals a dynamic network of interdependencies between the entities. Sincedynamic network inference is a computationally expensive task, we derive ascalable message-passing algorithm based on the Alternating Direction Method ofMultipliers (ADMM) to solve this problem in an efficient way. We also discussseveral extensions, including a streaming algorithm to update the model andincorporate new observations in real time. Finally, we evaluate our TVGLalgorithm on both real and synthetic datasets, obtaining interpretable resultsand outperforming state-of-the-art baselines in terms of both accuracy andscalability.

Network Inference via the Time-Varying Graphical Lasso