Generative Models of Information Diffusion with Asynchronous Timedelay

We address the problem of formalizing an information diffusion process on a social network as a generative model in the machine learning framework so that we can learn model parameters from the observation. Time delay plays an important role in formulating the likelihood function as well as for the analyses of information diffusion. We identified that there are two different types of time delay: link delay and node delay. The former corresponds to the delay associated with information propagation, and the latter corresponds to the delay due to human action. We further identified that there are two distinctions of the way the activation from the multiple parents is updated: nonoverride and override. The former sticks to the initial activation and the latter can decide to update the time to activate multiple times. We formulated the likelihood function of the well known diffusion models: independent cascade and linear threshold, both enhanced with asynchronous time delay distinguishing the difference in two types of delay and two types of update scheme. Simulation using four real world networks reveals that there are differences in the spread of information diffusion and they strongly depend on the choice of the parameter values and the denseness of the network.