General linear threshold models with application to influence maximization

Abstract: A number of models have been developed for information spread through networks, often for solving the Influence Maximization (IM) problem. IM is the task of choosing a fixed number of nodes to "seed" with information in order to maximize the spread of this information through the network, with applications in areas such as marketing and public health. Most methods for this problem rely heavily on the assumption of known strength of connections between network members (edge weights), which is often unrealistic. In this paper, we develop a likelihood-based approach to estimate edge weights from the fully and partially observed information diffusion paths. We also introduce a broad class of information diffusion models, the general linear threshold (GLT) model, which generalizes the well-known linear threshold (LT) model by allowing arbitrary distributions of node activation thresholds. We then show our weight estimator is consistent under the GLT and some mild assumptions. For the special case of the standard LT model, we also present a much faster expectation-maximization approach for weight estimation. Finally, we prove that for the GLT models, the IM problem can be solved by a natural greedy algorithm with standard optimality guarantees if all node threshold distributions have concave cumulative distribution functions. Extensive experiments on synthetic and real-world networks demonstrate that the flexibility in the choice of threshold distribution combined with the estimation of edge weights significantly improves the quality of IM solutions, spread prediction, and the estimates of the node activation probabilities.