Learning Social Infectivity in Sparse Low-rank Networks Using Multi-dimensional Hawkes Processes

How will the behaviors of individuals in a social network be influenced by their neighbors, the authorities and the communities? Such knowledge is often hidden from us and we only observe its manifestation in the form of recurrent and time-stamped events occurring at the individuals involved. It is an important yet challenging problem to infer the network of social inference based on the temporal patterns of these historical events. We propose a convex optimization approach to discover the hidden network of social influence by modeling the recurrent events at different individuals as multi-dimensional Hawkes processes. Furthermore, our estimation procedure, using nuclear and \ell_1 norm regularization simultaneously on the parameters, is able to take into account the prior knowledge of the presence of neighbor interaction, authority influence, and community coordination. To efficiently solve the problem, we also design an algorithm ADM4 which combines techniques of alternating direction method of multipliers and majorization minimization. We experimented with both synthetic and real world data sets, and showed that the proposed method can discover the hidden network more accurately and produce a better predictive model.