Hyper Hawkes Processes: Interpretable Models of Marked Temporal Point Processes

TL;DR

The paper introduces hyper Hawkes processes, a new family of marked temporal point process models that combine high predictive performance with interpretability by extending classical Hawkes processes with latent spaces and hypernetworks.

Contribution

It presents the hyper Hawkes process (HHP), a novel model family that enhances interpretability and flexibility while achieving state-of-the-art performance in benchmark tasks.

Findings

Achieves state-of-the-art performance on benchmark tasks.

Retains interpretability through linearity and structure of the original Hawkes process.

Provides tools for inspecting and understanding model predictions.

Abstract

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.