Ergodic opinion dynamics over networks: learning influences from partial observations

In this paper we address the problem of inferring direct influences in social networks from partial samples of a class of opinion dynamics. The interest is motivated by the study of several complex systems arising in social sciences, where a population of agents interacts according to a communication graph. These dynamics over networks often exhibit an oscillatory behavior, given the stochastic effects or the random nature of the local interactions process. Inspired by recent results on estimation of vector autoregressive processes, we propose a method to estimate the social network topology and the strength of the interconnections starting from partial observations of the interactions, when the whole sample path cannot be observed due to limitations of the observation process. Besides the design of the method, our main contributions include a rigorous proof of the convergence of the proposed estimators and the evaluation of the performance in terms of complexity and number of sample. Extensive simulations on randomly generated networks show the effectiveness of the proposed technique.