Fast Estimation of Causal Interactions using Wold Processes

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.