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 lowrank 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.

Authors

• RŽmi Lemonnier
• Kevin Scaman Inria Paris - Département d’informatique de l’ENS, PSL Research University
• Argyris Kalogeratos

Keywords

No keywords are indexed for this paper.