[论文解读] Ex ante prediction of cascade sizes on networks of agents facing binary outcomes

Paul Ormerod, Ellie Evans|arXiv (Cornell University)|Mar 17, 2011

Complex Network Analysis Techniques参考文献 23被引用 4

一句话总结

本文提出了一种在基于阈值和社交影响的网络中对级联规模进行事前预测的模型。通过使用种子连通性与个体阈值的逻辑回归，该模型在无标度网络中最高可解释46%的方差，表明阈值信息——尤其是易受影响个体的阈值——是预测能力的主要驱动力，支持了Watts和Dodds关于级联动态的猜想。

ABSTRACT

We consider in this paper the potential for ex ante prediction of the cascade size in a model of binary choice with externalities (Schelling 1973, Watts 2002). Agents are connected on a network and can be in one of two states of the world, 0 or 1. Initially, all are in state 0 and a small number of seeds are selected at random to switch to state1. A simple threshold rule specifies whether other agents switch subsequently. The cascade size (the percolation) is the proportion of all agents which eventually switches to state 1. We select information on the connectivity of the initial seeds, the connectivity of the agents to which they are connected, the thresholds of these latter agents, and the thresholds of the agents to which these are connected. We obtain results for random, small world and scale -free networks with different network parameters and numbers of initial seeds. The results are robust with respect to these factors. We perform least squares regression of the logit transformation of the cascade size (Hosmer and Lemeshow 1989) on these potential explanatory variables. We find considerable explanatory power for the ex ante prediction of cascade sizes. For the random networks, on average 32 per cent of the variance of the cascade sizes is explained, 40 per cent for the small world and 46 per cent for the scale-free. The connectivity variables are hardly ever significant in the regressions, whether relating to the seeds themselves or to the agents connected to the seeds. In contrast, the information on the thresholds of agents contains much more explanatory power. This supports the conjecture of Watts and Dodds (2007.) that large cascades are driven by a small mass of easily influenced agents.

研究动机与目标

• 调查在级联发生前预测网络化二元选择模型中级联规模的可行性。
• 识别哪些网络层面和个体层面的特征最能预测信息或行为级联的最终规模。
• 检验种子连通性与个体阈值中哪一个对事前预测更具信息量。
• 评估预测模型在不同网络拓扑结构（随机、小世界、无标度）下的鲁棒性。

提出的方法

• 研究使用二元选择阈值规则对网络中的个体行为进行建模，当个体受到足够多邻居影响时，其状态将从0切换到1。
• 随机选择初始种子，使其切换到状态1，从而根据个体阈值触发级联。
• 解释变量包括种子的连通性、其邻居的连通性，以及邻居和二阶邻居的阈值。
• 对级联规模进行logit变换，并使用最小二乘法对这些变量进行回归，以实现对级联结果的事前预测。
• 分析在具有不同参数和初始种子数量的随机、小世界和无标度网络中进行。
• 通过回归模型解释的级联规模方差比例来评估模型性能。

实验结果

研究问题

• RQ1 能否在事前以有意义的准确性预测网络化二元选择模型中的级联规模？
• RQ2 哪些网络层面和个体层面的特征——连通性或阈值——最能预测级联结果？
• RQ3 预测能力在随机、小世界和无标度等不同网络拓扑结构中如何变化？
• RQ4 与种子直接相连的个体或其邻居的阈值在多大程度上贡献于预测准确性？
• RQ5 阈值数据的预测能力在不同网络参数和初始种子数量下是否保持一致？

主要发现

• 该模型在随机网络中平均解释32%的级联规模方差，在小世界网络中为40%，在无标度网络中为46%。
• 与连通性相关的变量——如种子度数或邻居连通性——在回归模型中统计显著性很低或无显著性。
• 与种子相连的个体及其邻居的阈值信息占预测能力的绝大部分。
• 研究结果支持Watts和Dodds（2007）的猜想，即大规模级联由少数高度易感的个体驱动。
• 该预测模型在不同网络类型、参数和初始种子数量下均保持鲁棒性。
• 连通性变量不显著，表明仅靠网络结构不足以实现预测；个体阈值是主导因素。