analiza aiqbench
This paper introduces the Gaussian Process Discrete Hawkes Process (GP-DHP), a novel statistical framework designed to model self-exciting count data in discrete time bins. By employing collapsed Gaussian-process priors and finite-rank factorization, it enables efficient maximum a posteriori estimation without computationally expensive covariance matrix operations. The method demonstrates superior predictive accuracy across diverse real-world datasets, including disease surveillance, gun violence counts, and terrorism incidents.
A Semiparametric Discrete Hawkes Model with a Collapsed Gaussian-Process Prior
arXiv:2509.21996v3 Announce Type: replace-cross Abstract: Hawkes processes are used in settings where past events increase the likelihood of future events occurring, resulting in a natural clustering structure. Traditional Hawkes process models treat events as occurring in continuous time, but in many applications only the number of events occurring within a sequence of time bins is observed. We propose the Gaussian Process Discrete Hawkes Process (GP-DHP), a semiparametric model for discrete-time self-exciting count data that places Gaussian-process priors on both the baseline and the excitation. Marginalizing the two GP components induces a single latent Gaussian trajectory. A finite-rank factorization of this collapsed prior permits maximum a posteriori (MAP) estimation without forming or factorizing a \(T\times T\) covariance matrix. External covariates can enter the baseline through the same construction. In simulations, GP-DHP recovers diverse excitation shapes and evolving baselines. In applications to weekly disease surveillance (Singapore dengue and German cryptosporidiosis), daily shooting counts (New York City and the Gun Violence Archive), and a daily worldwide terrorism-incident series, it attains the best held-out predictive accuracy on four of the five series and, on the fifth, an accuracy not significantly different from the best.
Abstract:Hawkes processes are used in settings where past events increase the likelihood of future events occurring, resulting in a natural clustering structure. Traditional Hawkes process models treat events as occurring in continuous time, but in many applications only the number of events occurring within a sequence of time bins is observed. We propose the Gaussian Process Discrete Hawkes Process (GP-DHP), a semiparametric model for discrete-time self-exciting count data that places Gaussian-process priors on both the baseline and the excitation. Marginalizing the two GP components induces a single latent Gaussian trajectory. A finite-rank factorization of this collapsed prior permits maximum a posteriori (MAP) estimation without forming or factorizing a \(T\times T\) covariance matrix. External covariates can enter the baseline through the same construction. In simulations, GP-DHP recovers diverse excitation shapes and evolving baselines. In applications to weekly disease surveillance (Singapore dengue and German cryptosporidiosis), daily shooting counts (New York City and the Gun Violence Archive), and a daily worldwide terrorism-incident series, it attains the best held-out predictive accuracy on four of the five series and, on the fifth, an accuracy not significantly different from the best.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2509.21996 [stat.ML]
(or arXiv:2509.21996v3 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2509.21996 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 280 cuvinte
Subiecte conexe
Lattice-Based Cryptography Explained
Quantum Zeitgeist · 15 aug. 2026
Reflections on unlearning and inoculation
LessWrong · 20 sept. 2026
E-MoE: Enhanced Mixture-of-Experts for Non-Factorized Diffusion Language Models
arXiv · 1 oct. 2026
Productionizing TurboQuant on AMD GPUs for KV-Cache-Bound LLM Inference
AMD · 11 iun. 2026