Multivariate hawkes processes for large-scale inference

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 Scalable Low-Rank Hawkes Process (SLRHP) framework introduces a low-rank approximation of the kernel matrix that allows to perform the nonparametric learning of the d² triggering kernels in 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 require O(nd²) operations. Furthermore, the low-rank approximation allows SLRHP to learn representative patterns of interaction between event types, which is usually valuable for the analysis of complex processes in real-world networks.