Bayesian Inference of Network Structure From Information Cascades
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 <inline-formula><tex-math notation="LaTeX">$P(G)$</tex-math></inline-formula> conditioned on the observation of a set of infections <inline-formula><tex-math notation="LaTeX">$C$</tex-math></inline-formula>. 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.