Work

Learning Generalization and Regularization of Nonhomogeneous Temporal Poisson Processes

Year: 2024

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2402.12808

Authors: Van, Son Nguyen, Xuan, Hoai Nguyen

Institutions: Trường Đại học Khoa học và Công nghệ Hà Nội, Hanoi University of Science and Technology, HUTECH University

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4392020051

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