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.

翻译：在基于阈值动力学的社交网络中，当受到足够多同伴影响时，智能体会改变观点。现有文献通常假设网络结构和动力学完全已知，但这往往不切实际。本文研究如何从智能体同步观点更新的样本中学习网络结构。首先，若观点动力学遵循固定数量影响者阻止观点改变的阈值规则（如一致性和准一致性），我们提出了一种高效的PAC学习算法，前提是每个智能体的影响者数量有界。其次，在标准计算复杂性假设下，我们证明若智能体的观点遵循其影响者的多数意见，则不存在高效的PAC学习算法。我们提出了一种多项式时间启发式算法，在随机图上的模拟中，该算法成功学习到一致网络的比例超过98%，且在特定的智能体数量与观点扩散样本数量条件下未出现任何失败案例。