Learning Generalization and Regularization of Nonhomogeneous Temporal Poisson Processes
<|reference_start|>Learning Generalization and Regularization of Nonhomogeneous Temporal Poisson Processes: The Poisson process, especially the nonhomogeneous Poisson process (NHPP), is an essentially important counting process with numerous real-world applications. Up to date, almost all works in the literature have been on the estimation of NHPPs with infinite data using non-data driven binning methods. In this paper, we formulate the problem of estimation of NHPPs from finite and limited data as a learning generalization problem. We mathematically show that while binning methods are essential for the estimation of NHPPs, they pose a threat of overfitting when the amount of data is limited. We propose a framework for regularized learning of NHPPs with two new adaptive and data-driven binning methods that help to remove the ad-hoc tuning of binning parameters. Our methods are experimentally tested on synthetic and real-world datasets and the results show their effectiveness.<|reference_end|>
@article{van2024learning,
    title={Learning Generalization and Regularization of Nonhomogeneous Temporal
  Poisson Processes},
    author={Son Nguyen Van and Hoai Nguyen Xuan},
    journal={arXiv preprint arXiv:2402.12808},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.12808},
    primaryClass={cs.LG stat.ML}
}