Negative-binomial ensemble filtering for discrete-time Hawkes network reconstruction
Abstract
We develop a sequential ensemble filter for reconstructing directed excitation networks from overdispersed multivariate counts observed on a regular time grid. The data-generating model is a discrete-time negative-binomial Hawkes process, for which we prove exact first- and second-moment stability conditions and derive a row-wise sufficient condition. The filter learns the network and the dispersion online, and a row-composition parameter forecast keeps enough ensemble variation to respond to structural change. In synthetic experiments, we demonstrate that a Poisson-based filter provides comparable point-estimate accuracy of the network, while the proposed filter provides substantially better calibrated predictive and parameter uncertainty. Under an abrupt redistribution of influence, the filter recovers connections that are absent before the change. An application to daily property-crime counts in sixteen Chicago community areas gives broadly calibrated one-step predictions and a recovered network consistent with independent temporal and geographic information.
Related
- Stein's method for negative binomial and hyper-negative-binomial laws, with applications
- A new Bernstein-binomial model for fitting finite discrete data with over-dispersion: Likelihood-based and Bayesian approaches
- A Data-Consistent Approach to Ensemble Filtering
- A spatiotemporal negative binomial model with dynamic dispersion: An application to Tuberculosis infections
- Regularity-informed data assimilation: A hierarchical Bayesian approach to ensemble Kalman filtering for hyperbolic conservation laws
BibTeX
@misc{santitissadeekorn2026negativebinomial,
title = {{Negative-binomial ensemble filtering for discrete-time Hawkes network reconstruction}},
author = {Naratip Santitissadeekorn},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22742},
eprint = {2610.22742},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22742},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Negative-binomial ensemble filtering for discrete-time Hawkes network reconstruction
AU - Naratip Santitissadeekorn
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22742
UR - https://arxiv.org/abs/2610.22742
AB - We develop a sequential ensemble filter for reconstructing directed excitation networks from overdispersed multivariate counts observed on a regular time grid. The data-generating model is a discrete-time negative-binomial Hawkes process, for which we prove exact first- and second-moment stability conditions and derive a row-wise sufficient condition. The filter learns the network and the dispersion online, and a row-composition parameter forecast keeps enough ensemble variation to respond to structural change. In synthetic experiments, we demonstrate that a Poisson-based filter provides comparable point-estimate accuracy of the network, while the proposed filter provides substantially better calibrated predictive and parameter uncertainty. Under an abrupt redistribution of influence, the filter recovers connections that are absent before the change. An application to daily property-crime counts in sixteen Chicago community areas gives broadly calibrated one-step predictions and a recovered network consistent with independent temporal and geographic information.
ER -