Deep Linear Hawkes Processes

Yuxin Chang, Alex James Boyd, Cao Xiao, Taha Kass-Hout, Parminder Bhatia, Padhraic Smyth, Andrew Warrington

Keywords: Marked temporal point processes, state-space models, Hawkes processes

Abstract: Marked temporal point processes (MTPPs) are used to model sequences of different types of events with irregular arrival times, with broad applications ranging from healthcare and social networks to finance. We address shortcomings in existing point process models by drawing connections between modern deep state-space models (SSMs) and linear Hawkes processes (LHPs), culminating in an MTPP we call the _deep linear Hawkes process_ (DLHP). The DLHP modifies the linear differential equations in deep SSMs to be stochastic jump differential equations, akin to LHPs. After discretizing, the resulting recurrence can be implemented efficiently using a parallel scan. This brings both linear scaling and parallelism to MTPP models. This contrasts with attention-based MTPPs, which scale quadratically, and RNN-based MTPPs, which do not parallelize across the sequence length. We show empirically that DLHPs match or outperform existing models across a broad range of metrics on eight real-world datasets. Our proposed DLHP model is the first instance of the unique architectural capabilities of SSMs being leveraged to construct a new class of MTPP models.

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Submission Number: 3981