Multivariate Hawkes Processes for Large-Scale Inference

Abstract

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.

A Metric Space for Point Process Excitations

“…Recent progress has been made in factorizing interactions with a direct focus on scalability (Nickel & Le, 2020), improving on prior work in low-rank processes (Lemonnier et al, 2017). Block models on observed interaction pairs also exist (Junuthula et al, 2019).…”

“…One active line of work, paralleling ours, embeds each event based on some conceived heuristic like temporal proximity (Torricelli, Karsai, & Gauvin, 2020;Zhu & Xie, 2019;Zuo, Liu, Lin, Guo, Hu, & Wu, 2018); another direction of inquiry entails the estimation of lowrank multivariate Hawkes processes (Nickel & Le, 2020;Lemonnier, Scaman, & Kalogeratos, 2017;Junuthula, Haghdan, Xu, & Devabhaktuni, 2019). We differ from both in learning an actual metric-space representation vis-à-vis the real Hawkes likelihood.…”

Relaxed Clustered Hawkes Process for Student Procrastination Modeling in MOOCs

“…Other relevant literature on Hawkes processes mainly falls into 3 categories: (1) Multi-variate Hawkes processes that focus on modeling the mutual excitation among sequences (Zhou, Zha, and Song 2013;Luo et al 2015;Bacry et al 2020;Lemonnier, Scaman, and Kalogeratos 2017). (2) Uni-variate Hawkes models that model each sequence independently and discard the potential relatedness among all sequences, thus cannot infer sequence's future when its history is not observed e.g.…”