Network Generating Processes With Self Exciting Arrival Times

2025-05-28

AI Summary

To address the challenges of modeling long-range dependencies and historical sensitivity in continuous-time dynamic networks, this paper proposes the first generative framework that embeds path-dependent marked Hawkes processes into the network evolution space. Methodologically, it employs a nonlinear, left-continuous conditional intensity function to jointly model structural and temporal evolution driven by self-exciting events, integrating continuous-time point process theory with numerical likelihood estimation techniques. Theoretically, we establish stability criteria for the proposed model; algorithmically, we design an efficient simulation procedure and a scalable parameter inference scheme. Experiments on conference social network data demonstrate that the model accurately captures the dynamic evolution of participant relationships, achieving statistically significant improvements over state-of-the-art baselines in both predictive accuracy and interpretability.

Technology Category

Reasoning under Uncertainty: Relational Probabilistic ModelsData Mining & Knowledge Management: Graph Mining, Social Network Analysis & CommunityCognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsWeb Mining and Content Analysis: Models for Web evolutionSocial Networks and Social Media: Generative AI / large language models and their impact on social systems

Abstract

In this paper, we propose a novel modeling framework for time-evolving networks allowing for long-term dependence in network features that update in continuous time. Dynamic network growth is functionally parameterized via the conditional intensity of a marked point process. This characterization enables flexible modeling of both the time of updates and the network updates themselves, dependent on the entire left-continuous sample path. We propose a path-dependent nonlinear marked Hawkes process as an expressive platform for modeling such data; its dynamic mark space embeds the time-evolving network. We establish stability conditions, demonstrate simulation and subsequent feasible likelihood-based inference through numerical study, and present an application to conference attendee social network data. The resulting methodology serves as a general framework that can be readily adapted to a wide range of network topologies and point process model specifications.

Problem

• Modeling time-evolving networks with long-term dependence
• Flexible parameterization of dynamic network growth via marked point processes
• Developing a nonlinear Hawkes process for path-dependent network updates

Innovation

• Dynamic network growth via marked point process
• Path-dependent nonlinear marked Hawkes process
• Flexible modeling of time-evolving networks