Neural Spectral Marked Point Processes

TL;DR

This paper introduces a flexible neural network-based non-stationary influence kernel for point processes, enabling modeling of complex, context-dependent event data with theoretical guarantees and superior empirical performance.

Contribution

It proposes a novel neural spectral kernel for non-stationary marked point processes, enhancing modeling capacity over traditional stationary kernels.

Findings

Outperforms state-of-the-art methods on synthetic data

Effective in modeling complex, non-stationary event data

Provides theoretical guarantees for performance

Abstract

Self- and mutually-exciting point processes are popular models in machine learning and statistics for dependent discrete event data. To date, most existing models assume stationary kernels (including the classical Hawkes processes) and simple parametric models. Modern applications with complex event data require more general point process models that can incorporate contextual information of the events, called marks, besides the temporal and location information. Moreover, such applications often require non-stationary models to capture more complex spatio-temporal dependence. To tackle these challenges, a key question is to devise a versatile influence kernel in the point process model. In this paper, we introduce a novel and general neural network-based non-stationary influence kernel with high expressiveness for handling complex discrete events data while providing theoretical performance guarantees. We demonstrate the superior performance of our proposed method compared with the state-of-the-art on synthetic and real data.