In this paper, we propose a technique for the estimation of the influence
matrix in a sparse social network, in which n individual communicate in a
gossip way. At each step, a random subset of the social actors is active and
interacts with randomly chosen neighbors. The opinions evolve according to a
Friedkin and Johnsen mechanism, in which the individuals updates their belief
to a convex combination of their current belief, the belief of the agents they
interact with, and their initial belief, or prejudice. Leveraging recent
results of estimation of vector autoregressive processes, we reconstruct the
social network topology and the strength of the interconnections starting from
\textit{partial observations} of the interactions, thus removing one of the
main drawbacks of finite horizon techniques. The effectiveness of the proposed
method is shown on randomly generation networks