Community Structure Recovery and Interaction Probability Estimation for Gossip Opinion Dynamics

TL;DR

This paper presents a method to simultaneously recover community structures and estimate interaction probabilities in gossip opinion dynamics models, demonstrating finite-time recovery and almost sure convergence of estimators.

Contribution

It introduces a joint recovery and estimation algorithm for community labels and interaction probabilities based on a single trajectory, with proven convergence and sample complexity analysis.

Findings

Community recovery achieved in finite time

Interaction estimator converges almost surely

Sample complexity bounds established

Abstract

We study how to jointly recover the community structure and estimate the interaction probabilities of gossip opinion dynamics. In this process, agents randomly interact pairwise, and there are stubborn agents never changing their states. Such a model illustrates how disagreement and opinion fluctuation arise in a social network. It is assumed that each agent is assigned with one of two community labels, and the agents interact with probabilities depending on their labels. The considered problem is to jointly recover the community labels of the agents and estimate interaction probabilities between the agents, based on a single trajectory of the model. We first study stability and limit theorems of the model, and then propose a joint recovery and estimation algorithm based on a trajectory. It is verified that the community recovery can be achieved in finite time, and the interaction estimator converges almost surely. We derive a sample-complexity result for the recovery, and analyze the estimator's convergence rate. Simulations are presented for illustration of the performance of the proposed algorithm.