面向八卦舆论动力学的社区结构恢复与交互概率估计
Community Structure Recovery and Interaction Probability Estimation for Gossip Opinion Dynamics
AI总结：
针对带顽固智能体的八卦舆论动力学，提出基于单条轨迹的联合社区恢复与交互概率估计算法，证明有限时间恢复与几乎必然收敛，推导样本复杂度与收敛速率并通过仿真验证。
摘要：
我们研究如何联合恢复八卦舆论动力学的社区结构并估计其交互概率。在该过程中，智能体两两随机交互，且存在从不改变自身状态的顽固智能体。这类模型阐释了社交网络中分歧与舆论波动的产生机制。我们假设每个智能体被赋予两个社区标签中的一个，且智能体间的交互概率取决于其标签。所研究的问题是：基于该模型的单条轨迹，联合恢复智能体的社区标签并估计智能体间的交互概率。我们首先研究了模型的稳定性与极限定理，随后提出了一种基于轨迹的联合恢复与估计算法。经证明，社区恢复可在有限时间内完成，且交互估计量几乎必然收敛。我们推导了恢复的样本复杂度结果，并分析了估计量的收敛速率。我们还通过仿真验证了所提算法的性能。
英文摘要：
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.
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