A General Marked Point Process Framework For Self-Exciting Network Evolution
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908898517057536 |
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| author | Clark, Duncan A Kresin, Conor J. Jones-Todd, Charlotte M. |
| author_facet | Clark, Duncan A Kresin, Conor J. Jones-Todd, Charlotte M. |
| contents | 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, joint modeling of both update timing 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 prove well-posedness and establish sufficient stability conditions, demonstrate simulation and subsequent feasible likelihood-based inference through numerical study, and illustrate the methodology with an application to conference attendee social network data. The proposed formulation provides a flexible and principled foundation for statistical inference on complex network evolution in continuous time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22659 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A General Marked Point Process Framework For Self-Exciting Network Evolution Clark, Duncan A Kresin, Conor J. Jones-Todd, Charlotte M. Methodology 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, joint modeling of both update timing 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 prove well-posedness and establish sufficient stability conditions, demonstrate simulation and subsequent feasible likelihood-based inference through numerical study, and illustrate the methodology with an application to conference attendee social network data. The proposed formulation provides a flexible and principled foundation for statistical inference on complex network evolution in continuous time. |
| title | A General Marked Point Process Framework For Self-Exciting Network Evolution |
| topic | Methodology |
| url | https://arxiv.org/abs/2505.22659 |