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Identifying the topology underlying a set of time series is useful for taskssuch as prediction, denoising, and data completion. Vector autoregressive (VAR)model-based topologies capture dependencies among time series and are ofteninferred from observed spatio-temporal data. When data are affected by noiseand/or missing samples, topology identification and signal recovery(reconstruction) tasks must be performed jointly. Additional challenges arisewhen i) the underlying topology is time-varying, ii) data become availablesequentially, and iii) no delay is tolerated. This study proposes an onlinealgorithm to overcome these challenges in estimating VAR model-basedtopologies, having constant complexity per iteration, which makes itinteresting for big-data scenarios. The inexact proximal online gradientdescent framework is used to derive a performance guarantee for the proposedalgorithm, in the form of a dynamic regret bound. Numerical tests are alsopresented, showing the ability of the proposed algorithm to track time-varyingtopologies with missing data in an online fashion.

Online Joint Topology Identification and Signal Estimation from Streams with Missing Data