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.

Automated summary

This article formulates the positive link prediction problem in a system identification framework, using dynamic graphical models for autoregressive moving-average (ARMA) Gaussian random processes. The network is modeled on two different time scales: a faster scale assuming stationary dynamics of the agents, and a slower scale accounting for possible appearance of new edges. The identification problem is cast into an optimization framework that generalizes existing methods for ARMA graphical model identification. The article proves the existence and uniqueness of the solution and proposes a numerical computation procedure. Simulation results are provided to test the method's performance.