Andrew Warrington

Alex Boyd, Andrew Warrington, Taha Kass-Hout et al.

Foundational marked temporal point process (MTPP) models, such as the Hawkes process, often use inexpressive model families in order to offer interpretable parameterizations of event data. On the other hand, neural MTPPs models forego this interpretability in favor of absolute predictive performance. In this work, we present a new family MTPP models: the hyper Hawkes process (HHP), which aims to be as flexible and performant as neural MTPPs, while retaining interpretable aspects. To achieve this, the HHP extends the classical Hawkes process to increase its expressivity by first expanding the dimension of the process into a latent space, and then introducing a hypernetwork to allow time- and data-dependent dynamics. These extensions define a highly performant MTPP family, achieving state-of-the-art performance across a range of benchmark tasks and metrics. Furthermore, by retaining the linearity of the recurrence, albeit now piecewise and conditionally linear, the HHP also retains much of the structure of the original Hawkes process, which we exploit to create direct probes into how the model creates predictions. HHP models therefore offer both state-of-the-art predictions, while also providing an opportunity to ``open the box'' and inspect how predictions were generated.

Yuxin Chang, Alex Boyd, Cao Xiao et al.

Marked temporal point processes (MTPPs) model sequences of events occurring at irregular time intervals, with wide-ranging applications in fields such as healthcare, finance and social networks. We propose the state-space point process (S2P2) model, a novel and performant model that leverages techniques derived for modern deep state-space models (SSMs) to overcome limitations of existing MTPP models, while simultaneously imbuing strong inductive biases for continuous-time event sequences that other discrete sequence models (i.e., RNNs, transformers) do not capture. Inspired by the classical linear Hawkes processes, we propose an architecture that interleaves stochastic jump differential equations with nonlinearities to create a highly expressive intensity-based MTPP model, without the need for restrictive parametric assumptions for the intensity. Our approach enables efficient training and inference with a parallel scan, bringing linear complexity and sublinear scaling while retaining expressivity to MTPPs. Empirically, S2P2 achieves state-of-the-art predictive likelihoods across eight real-world datasets, delivering an average improvement of 33% over the best existing approaches.