Randomized opinion dynamics over networks: influence estimation from partial observations

TL;DR

This paper introduces a method to estimate influence matrices in sparse social networks with partial observations, using opinion dynamics models and autoregressive process estimation, enabling network reconstruction from limited data.

Contribution

It presents a novel approach combining opinion dynamics and autoregressive estimation to reconstruct social network topology from partial interaction data.

Findings

Effective reconstruction of influence matrices demonstrated on synthetic networks.

Method reduces reliance on full observation data, improving practicality.

Shows robustness in sparse, randomly generated networks.

Abstract

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.