A generalization error bound for sparse and low-rank multivariate Hawkes processes

Understanding the dynamics of social interactions is a challenging problem of fastly growing interest [11, 20, 9, 21] because of the large number of applications in web-advertisement and e-commerce, where large-scale logs of event history are available. A common supervised approach consists in the prediction of labels based on declared interactions (friendship, like, follower, etc.) However such supervision is not always available, and it does not always describe accurately the level of interactions between users. Labels are often only binary while a quantification of the interaction is more interesting, declared interactions are often deprecated, and more generally a supervised approach is not enough to infer the latent communities of users, as temporal patterns of actions of users are much more informative. A recent set of papers [32, 14, 10] consider an approach for recovering latent social groups directly based on the real actions or events of users, called also nodes in the following, that uses only the timestamps patterns of the considered events. The models assume a structure of data consisting in a sequence of independent cascades, containing timestamps for each nodes.