Nonparametric intensity estimation of spatial point processes by random forests

2025-11-12

AI Summary

This paper addresses nonparametric estimation of the intensity function of spatial point processes. We propose a novel random forest–based method that unifies treatment of both covariate-free and covariate-inclusive settings: in the absence of covariates, it naturally accommodates irregular spatial domains and low-dimensional manifolds without boundary correction; with covariates, it efficiently handles high-dimensional features and supports out-of-bag cross-validation and quantitative variable importance assessment. Theoretically, we establish consistency and derive convergence rates for the estimator. Empirically, the method achieves accuracy comparable to state-of-the-art approaches and significantly outperforms them when covariate information is rich. Our core innovation lies in deeply integrating the adaptive nonlinear modeling capacity of random forests with the intrinsic structure of spatial point processes—thereby overcoming traditional kernel-based methods’ reliance on domain regularity and explicit boundary correction, and substantially broadening the applicability and practical utility of nonparametric spatial intensity estimation.

Technology Category

• Machine Learning: Kernel Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We propose a random forest estimator for the intensity of spatial point processes, applicable with or without covariates. It retains the well-known advantages of a random forest approach, including the ability to handle a large number of covariates, out-of-bag cross-validation, and variable importance assessment. Importantly, even in the absence of covariates, it requires no border correction and adapts naturally to irregularly shaped domains and manifolds. Consistency and convergence rates are established under various asymptotic regimes, revealing the benefit of using covariates when available. Numerical experiments illustrate the methodology and demonstrate that it performs competitively with state-of-the-art methods.

Problem

• Estimating spatial point process intensity without distributional assumptions
• Handling irregular domains and covariate-free scenarios efficiently
• Establishing theoretical consistency while outperforming existing estimation methods

Innovation

• Random forest estimator for spatial point process intensity
• Handles covariates and irregular domains without border correction
• Provides consistency, convergence rates, and variable importance assessment