Before revision: Hawkes processes have been successfully applied to understand online information diffusion and popularity of online items. Most prior work concentrate on individually modeling successful diffusion cascades, while discarding smaller cascades which, however, account for a majority proportion of the available data. In this work , we propose a set of tools to leverage information in the small cascades: a joint fitting procedure that accounts for cascade size bias in the sample, a Borel mixture model and a clustering algorithm to uncover latent groups within these cascades , and the posterior final size distribution of Hawkes processes.
After revision: It is well-known that online behavior is long-tailed, with most cascaded actions being short and a few being very long. A prominent drawback in generative models for online events is the inability to describe unpopular items well. This work addresses these shortcomings by proposing dual mixture self-exciting processes to jointly learn from groups of cascades. We first start from the observation that maximum likelihood estimates for content virality and influence decay are separable in a Hawkes process. Next, our proposed model, which leverages a Borel mixture model and a clustering algorithm to uncover latent groups within these cascades , and the posterior final size distribution of Hawkes processes.