Statistical Estimation of Diffusion Network Topologies

Abstract

Reconstructing the topology of a diffusion network based on observed diffusion results is an open challenge in data mining. Existing approaches mostly assume that the observed diffusion results are available and consist of not only the final infection statuses of nodes, but also the exact timestamps that pinpoint when infections occur. Nonetheless, the exact infection timestamps are often unavailable in practice, due to a high cost and uncertainties in the monitoring of node infections. In this work, we investigate the problem of how to infer the topology of a diffusion network from only the final infection statuses of nodes. To this end, we propose a new scoring criterion for diffusion network reconstruction, which is able to estimate the likelihood of potential topologies of the objective diffusion network based on infection status results with a relatively low statistical error. As the proposed scoring criterion is decomposable, our problem is transformed into finding for each node in the network a set of most probable parent nodes that maximizes the value of a local score. Furthermore, to eliminate redundant computations during the search of most probable parent nodes, we identify insignificant candidate parent nodes by checking whether their infections have negative or extremely low positive correlations with the infections of a corresponding child node, and exclude them from the search space. Extensive experiments on both synthetic and real-world networks are conducted, and the results verify the effectiveness and efficiency of our approach.