Pareto cascade modeling of diffusion networks

Time plays an essential role in the diffusion of information, influence and disease over networks. Usually we are only able to collect cascade data in which an infection (receiving) time of each node is recorded but without any transmission information over the network. In this paper, we infer the transmission rates among nodes by Pareto distributions. Pareto modeling has several advantages. It is naturally motivated and has a nice interpretation. The scale parameter of a Pareto distribution naturally fits into the starting time of a transition, i.e., the infection time of a parent node in the cascade data is the starting point for a transition from the parent to its receiver. The shape parameter (alpha) serves as the transition rate. The larger the alpha is, the faster the transition is and there is a higher probability for disease or information to spread in a short time period. Pareto modeling is mathematically simple and computationally easy. It has explicit solutions for the optimization problem that maximizes time-dependent pairwise transmission likelihoods between all pairs of nodes. We present three modelings with a common transmission rate, with different transmission rates and with different infection rates. Experiments on real and synthetic data show that our models accurately estimate the transmission rates and perform better than the existing method.