In this paper, we present a framework for fitting multivariate Hawkes
processes for large-scale problems both in the number of events in the observed
history n and the number of event types d (i.e. dimensions). The proposed
Low-Rank Hawkes Process (LRHP) framework introduces a low-rank approximation of
the kernel matrix that allows to perform the nonparametric learning of the
d2 triggering kernels using at most O(ndr2) operations, where r is the
rank of the approximation (r≪d,n). This comes as a major improvement to
the existing state-of-the-art inference algorithms that are in O(nd2).
Furthermore, the low-rank approximation allows LRHP to learn representative
patterns of interaction between event types, which may be valuable for the
analysis of such complex processes in real world datasets. The efficiency and
scalability of our approach is illustrated with numerical experiments on
simulated as well as real datasets.Comment: 16 pages, 5 figure