To infer a diffusion network based on observations from historical diffusion processes, existing approaches assume that observation data contain exact occurrence time of each node infection, or at least the eventual infection statuses of nodes in each diffusion process. They determine potential influence relationships between nodes by identifying frequent sequences, or statistical correlations, among node infections. In some real-world settings, such as the spread of epidemics, tracing exact infection times is often infeasible due to a high cost; even obtaining precise infection statuses of nodes is a challenging task, since observable symptoms such as headache only partially reveal a node’s true status. In this work, we investigate how to effectively infer a diffusion network from observation data with uncertainty. Provided with only probabilistic information about node infection statuses, we formulate the problem of diffusion network inference as a constrained nonlinear regression w.r.t. the probabilistic data. An alternating maximization method is designed to solve this regression problem iteratively, and the improvement of solution quality in each iteration can be theoretically guaranteed. Empirical studies are conducted on both synthetic and real-world networks, and the results verify the effectiveness and efficiency of our approach.

To learn influence relationships between nodes in a diffusion network, most existing approaches resort to precise timestamps of historical node infections. The target network is customarily assumed as an one-aspect diffusion network, with homogeneous influence relationships. Nonetheless, tracing node infection timestamps is often infeasible due to high cost, and the type of influence relationships may be heterogeneous because of the diversity of propagation media. In this work, we study how to infer a multi-aspect diffusion network with heterogeneous influence relationships, using only node infection statuses that are more readily accessible in practice. Equipped with a probabilistic generative model, we iteratively conduct a posteriori, quantitative analysis on historical diffusion results of the network, and infer the structure and strengths of homogeneous influence relationships in each aspect. Extensive experiments on both synthetic and real-world networks are conducted, and the results verify the effectiveness and efficiency of our approach.

To reconstruct the topology of a diffusion network, existing approaches customarily demand not only eventual infection statuses of nodes, but also the exact times when infections occur. In real-world settings, such as the spread of epidemics, tracing the exact infection times is often infeasible; even obtaining the eventual infection statuses of all nodes is a challenging task. In this work, we study topology reconstruction of a diffusion network with incomplete observations of the node infection statuses. To this end, we iteratively infer the network topology based on observed infection statuses and estimated values for unobserved infection statuses by investigating the correlation of node infections, and learn the most probable probabilities of the infection propagations among nodes w.r.t. current inferred topology, as well as the corresponding probability distribution of each unobserved infection status, which in turn helps update the estimate of unobserved data. Extensive experimental results on both synthetic and real-world networks verify the effectiveness and efficiency of our approach.

To infer the structure of a diffusion network from observed diffusion results, existing approaches customarily assume that observed data are complete and contain the final infection status of each node, as well as precise timestamps of node infections. Due to high cost and uncertainties in the monitoring of node infections, exact timestamps are often unavailable in practice, and even the final infection statuses of nodes are sometimes missing. In this work, we study how to carry out diffusion network inference without infection timestamps, using only partial observations of the final infection statuses of nodes. To this end, we iteratively infer the structure of the target diffusion network with observed data and imputed values for missing data, and learn the most likely infection transmission probabilities between nodes w.r.t. current inferred structure, which then help us update the imputation of missing data in turn. Extensive experimental results on both synthetic and real-world networks show that our approach can properly handle missing data and accurately uncover diffusion network structures.

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.