On the Limits of PAC Learning of Networks from Opinion Dynamics

TL;DR

This paper investigates the learnability of social network opinion dynamics from samples, providing efficient algorithms for some models and proving hardness for others, with practical heuristics tested on simulations.

Contribution

It introduces a PAC learning algorithm for threshold-based opinion dynamics and demonstrates computational hardness for majority-based models, along with a successful heuristic approach.

Findings

Efficient PAC learning for threshold influence models with bounded influencers.

Proved no efficient PAC learning exists for majority influence models under standard assumptions.

Heuristic algorithm achieves over 98% success in learning networks in simulations.

Abstract

Agents in social networks with threshold-based dynamics change opinions when influenced by sufficiently many peers. Existing literature typically assumes that the network structure and dynamics are fully known, which is often unrealistic. In this work, we ask how to learn a network structure from samples of the agents' synchronous opinion updates. Firstly, if the opinion dynamics follow a threshold rule in which a fixed number of influencers prevent opinion change (e.g., unanimity and quasi-unanimity), we provide an efficient PAC learning algorithm provided that the number of influencers per agent is bounded. Secondly, under standard computational complexity assumptions, we prove that if agents' opinions follow the majority of their influencers, then there is no efficient PAC learning algorithm. We propose a polynomial-time heuristic that successfully learns consistent networks in over $98\%$ of our simulations on random graphs, with no failures for some specified conditions on the numbers of agents and opinion diffusion examples.