Before revision:  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. On a dataset of Twitter cascades, we show that , compared to the state-of-art models, the proposed method improves the generalization performance on unseen data, delivers better prediction for final popularity and provides means to characterize online content from the way Twitter users discuss about it .
After revision:  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 kernel mixture model, jointly models the unfolding of a heterogeneous set of cascades. When applied to cascades of the same online items, the model directly characterizes their spread dynamics and supplies interpretable quantities, such as content virality and content influence decay, as well as methods for predicting the final content popularities. On two retweet cascade datasets -- one relating to YouTube videos and the second relating to controversial news articles -- we show that , compared to the state-of-art models, the proposed method improves the generalization performance on unseen data, delivers better prediction for final popularity and provides means to characterize online content from the way Twitter users discuss about it .