Contagion processes are strongly linked to the network structures on which they propagate, and learning these structures is essential for understanding and intervention on complex network processes such as epidemics and (mis)information propagation. However, using contagion data to infer network structure is a challenging inverse problem. In particular, it is imperative to have appropriate measures to quantify uncertainty in network structure estimates; however, these are largely ignored in many optimisation based approaches. We present a probabilistic framework using samples from the distribution of networks that are compatible with the dynamics observed to produce network and uncertainty estimates. We demonstrate the method using the well known independent cascade model to sample from the distribution of networks $P(G)$ conditioned on the observation of a set of infections $C$ . We evaluate the accuracy of the method using the marginal probabilities of each edge in the distribution, and show the benefits of quantifying uncertainty to improve estimates and understanding, particularly with small amounts of data.

中文翻译：

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基于信息级联的贝叶斯网络结构推断

传染过程与传播它们的网络结构紧密相连，学习这些结构对于理解和干预诸如流行病和（错误）信息传播之类的复杂网络过程至关重要。但是，使用传染数据推断网络结构是一个具有挑战性的逆问题。特别是必须采取适当的措施来量化网络结构估计中的不确定性；但是，这些在许多基于优化的方法中都被忽略了。我们提出了一个概率框架，该模型使用了来自网络分布的样本，这些样本与观察到的产生网络和不确定性估计的动力学兼容。我们演示了使用众所周知的独立级联模型从网络分布中采样的方法$ P（G）$ 以观察一组感染为条件 $ C $ 。我们使用分布中每个边的边际概率评估该方法的准确性，并显示量化不确定性的好处，以改善估计和理解，尤其是在少量数据的情况下。