Prediction of Partially Observed Dynamical Processes Over Networks via Dictionary Learning

Prediction of dynamical processes evolving over network graphs is a basic task encountered in various areas of science and engineering. The prediction challenge is exacerbated when only partial network observations are available, that is when only measurements from a subset of nodes are available. To tackle this challenge, the present work introduces a joint topology- and data-driven approach for network-wide prediction able to handle partially observed network data. First, the known network structure and historical data are leveraged to design a dictionary for representing the network process. The novel approach draws from semi-supervised learning to enable learning the dictionary with only partial network observations. Once the dictionary is learned, network-wide prediction becomes possible via a regularized least-squares estimate which exploits the parsimony encapsulated in the design of the dictionary. Second, an online network-wide prediction algorithm is developed to jointly extrapolate the process over the network and update the dictionary accordingly. This algorithm is able to handle large training datasets at a fixed computational cost. More important, the online algorithm takes into account the temporal correlation of the underlying process, and thereby improves prediction accuracy. The performance of the novel algorithms is illustrated for prediction of real Internet traffic. There, the proposed approaches are shown to outperform competitive alternatives.