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Regularization techniques for inhomogeneous (spatial) point processes intensity and conditional intensity estimation.

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Title: Regularization techniques for inhomogeneous (spatial) point processes intensity and conditional intensity estimation.
Authors: Coeurjolly, Jean-Francois1 (AUTHOR), Ba, Ismaïla2 (AUTHOR), Choiruddin, Achmad3 (AUTHOR)
Source: ESAIM: Proceedings & Surveys. 2025, Vol. 80, p2-16. 15p.
Subjects: Point processes, Stochastic models, Stochastic processes
Abstract (English): Point processes are stochastic models generating interacting points or events in time and/or space. Among characteristics of these models, first-order intensity and conditional intensity functions are often considered. We focus on inhomogeneous parametric forms of these functions assumed to depend on a certain number of spatial covariates. When this number of covariates is large, we are faced with a high-dimensional problem. This paper provides an overview of these questions and existing solutions based on regularizations. [ABSTRACT FROM AUTHOR]
Abstract (French): Les processus ponctuels constituent une classe de modèles stochastiques permettant de modéliser des évènements dans le temps et/ou l'espace en interaction. Parmi les caractéristiques d'un processus ponctuel, l'intensitéet l'intensitéconditionnelle d'ordre un sont souvent considérées. Nous nous concentrons ici sur des formes paramétriques inhomogènes de ces fonctions que nous supposons dépendre d'un certain nombre de covariables spatiales. Lorsque ce nombre est élevé, nous faisons face à un problème de grande dimension. Ce papier a pour objectif de présenter un aperçu de ces problèmes et solutions existantes. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:Point processes are stochastic models generating interacting points or events in time and/or space. Among characteristics of these models, first-order intensity and conditional intensity functions are often considered. We focus on inhomogeneous parametric forms of these functions assumed to depend on a certain number of spatial covariates. When this number of covariates is large, we are faced with a high-dimensional problem. This paper provides an overview of these questions and existing solutions based on regularizations. [ABSTRACT FROM AUTHOR]
ISSN:22673059
DOI:10.1051/proc/202580002