Year: 2023
Type: preprint
Abstract: Point process models are widely used for continuous-time discrete-event data, where each data point includes time and additional information called "marks," such as locations, nodes, or event types. We present a new point process model for discrete-event data over networks, built upon Hawkes' classic influence-kernel formulation to capture the effects of historical events on the occurrence of future events. The key idea is to represent the influence kernel using graph neural networks (GNNs), thereby capturing the underlying graph structure while using the strong representation power of GNNs. Compared with prior work that directly models the conditional intensity function using neural networks, our kernel representation captures repeated patterns of event influence more effectively by combining statistical and deep learning models, leading to more efficient model estimation and better predictive performance. Our work significantly extends existing deep spatio-temporal kernels for point process data, which are inapplicable to our setting because their observation spaces are Euclidean rather than graph structured. We present comprehensive experiments on synthetic and real-world data to demonstrate the superior performance of the proposed approach over state-of-the-art methods in predicting future events and uncovering graph structure from the data.
Source: arXiv (Cornell University)
Institutions: Georgia Institute of Technology, Duke University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: ATD: Scanning Dynamic Spatial-Temporal Discrete Events for Threat Detection, Bridging Statistical Hypothesis Tests and Deep Learning for Reliability and Computational Efficiency, CAREER: Quick Detection for Streaming Data Over Dynamic Networks, G3387330441, G4324459455, Data-Driven Optimal Police Patrol Zone Districting and Staffing, Sequential Detection and Prediction for Solar Situation Awareness in Power Networks, AI Institute for Advances in Optimization, G6127310570, G6671297155, G7238632903, G7911581280, CAREER: Learning of graph diffusion and transport from high dimensional data with low-dimensional structures, G975068223
OpenAlex ID: W4381573434