Data-Driven Link Prediction Over Graphical Models

The positive link prediction problem is formulated in a system identification framework: We consider dynamic graphical models for autoregressive moving-average (ARMA) Gaussian random processes. For the identification of the parameters, we model our network on two different time scales: A quicker one, over which we assume that the process representing the dynamics of the agents can be considered to be stationary, and a slower one in which the model parameters may vary. The latter accounts for the possible appearance of new edges. The identification problem is cast into an optimization framework which can be seen as a generalization of the existing methods for the identification of ARMA graphical models. We prove the existence and uniqueness of the solution of such an optimization problem and we propose a procedure to compute numerically this solution. Simulations testing the performances of our method are provided.