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 d 2 triggering kernels in at most O ( ndr 2 ) 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 ( nd 2 ) 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.