Learning Parametric Models for Social Infectivity in Multi-Dimensional Hawkes Processes

Efficient and effective learning of social infectivity presents a critical challenge in modeling diffusion phenomena in social networks and other applications. Existing methods require substantial amount of event cascades to guarantee the learning accuracy and they only consider time-invariant infectivity. Our paper overcomes those two drawbacks by constructing a more compact model and parameterizing the infectivity using time-varying features, thus dramatically reduces the data requirement, and enables the learning of time-varying infectivity which also takes into account the underlying network topology. We replace the pairwise infectivity in the multidimensional Hawkes processes with linear combinations of those time-varying features, and optimize the associated coefficients with lasso-type of regularization. To efficiently solve the resulting optimization problem, we employ the technique of alternating direction method of multipliers which allows independent updating of the individual coefficients by optimizing a surrogate function upper-bounding the original objective function. On both synthetic and real world data, the proposed method performs better than alternatives in terms of both recovering the hidden diffusion network and predicting the occurrence time of social events.