Randomized opinion dynamics over networks: influence estimation from partial observations
For researchers studying opinion dynamics, this work removes the need for full observation of interactions, a key limitation of prior finite-horizon methods.
This paper proposes a technique to estimate the influence matrix in sparse social networks from partial observations of gossip-style interactions, using vector autoregressive estimation. The method is validated on randomly generated networks.
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.