  We here focus on the task of learning Granger causality matrices for
multivariate point processes. In order to accomplish this task, our work is the
first to explore the use of Wold processes. By doing so, we are able to develop
asymptotically fast MCMC learning algorithms. With $N$ being the total number
of events and $K$ the number of processes, our learning algorithm has a
$O(N(\,\log(N)\,+\,\log(K)))$ cost per iteration. This is much faster than the
$O(N^3\,K^2)$ or $O(K^3)$ for the state of the art. Our approach, called
GrangerBusca, is validated on nine datasets. This is an advance in relation to
most prior efforts which focus mostly on subsets of the Memetracker data.
Regarding accuracy, GrangerBusca is three times more accurate (in Precision@10)
than the state of the art for the commonly explored subsets Memetracker. Due to
GrangerBusca's much lower training complexity, our approach is the only one
able to train models for larger, full, sets of data.
