Link Prediction in Graphs with Autoregressive Features

In the paper, we consider the problem of link prediction in time-evolving graphs. We assume that certain graph features, such as the node degree, follow a vector autoregressive (VAR) model and we propose to use this information to improve the accuracy of prediction. Our strategy involves a joint optimization procedure over the space of adjacency matrices and VAR matrices which takes into account both sparsity and low rank properties of the matrices. Oracle inequalities are derived and illustrate the trade-offs in the choice of smoothing parameters when modeling the joint effect of sparsity and low rank property. The estimate is computed efficiently using proximal methods through a generalized forward-backward agorithm.