  Cascades are ubiquitous in various network environments. How to predict these
cascades is highly nontrivial in several vital applications, such as viral
marketing, epidemic prevention and traffic management. Most previous works
mainly focus on predicting the final cascade sizes. As cascades are typical
dynamic processes, it is always interesting and important to predict the
cascade size at any time, or predict the time when a cascade will reach a
certain size (e.g. an threshold for outbreak). In this paper, we unify all
these tasks into a fundamental problem: cascading process prediction. That is,
given the early stage of a cascade, how to predict its cumulative cascade size
of any later time? For such a challenging problem, how to understand the micro
mechanism that drives and generates the macro phenomenons (i.e. cascading
proceese) is essential. Here we introduce behavioral dynamics as the micro
mechanism to describe the dynamic process of a node's neighbors get infected by
a cascade after this node get infected (i.e. one-hop subcascades). Through
data-driven analysis, we find out the common principles and patterns lying in
behavioral dynamics and propose a novel Networked Weibull Regression model for
behavioral dynamics modeling. After that we propose a novel method for
predicting cascading processes by effectively aggregating behavioral dynamics,
and propose a scalable solution to approximate the cascading process with a
theoretical guarantee. We extensively evaluate the proposed method on a large
scale social network dataset. The results demonstrate that the proposed method
can significantly outperform other state-of-the-art baselines in multiple tasks
including cascade size prediction, outbreak time prediction and cascading
process prediction.
