Robust variable selection for spatial point processes observed with noise

2025-10-29

AI Summary

High-resolution remote sensing spatial point data commonly suffer from measurement errors and detection noise (e.g., spurious displacements, missed detections), undermining the robustness of conventional intensity function variable selection in spatial point processes. To address this, we propose a prior-free robust variable selection method that integrates stability selection with nonconvex optimal subset penalization, coupled with point process subsampling and sparse regularization. The approach is compatible with diverse spatial point process models—including Poisson and Thomas processes—and significantly improves both identification accuracy and selection stability of true covariates under multiple noise scenarios. Experiments on simulated data and real-world tropical forest tree distribution data demonstrate its reliability in recovering key environmental covariates. This provides a trustworthy modeling framework for mechanistic interpretation under noisy observational conditions.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

We propose a method for variable selection in the intensity function of spatial point processes that combines sparsity-promoting estimation with noise-robust model selection. As high-resolution spatial data becomes increasingly available through remote sensing and automated image analysis, identifying spatial covariates that influence the localization of events is crucial to understand the underlying mechanism. However, results from automated acquisition techniques are often noisy, for example due to measurement uncertainties or detection errors, which leads to spurious displacements and missed events. We study the impact of such noise on sparse point-process estimation across different models, including Poisson and Thomas processes. To improve noise robustness, we propose to use stability selection based on point-process subsampling and to incorporate a non-convex best-subset penalty to enhance model-selection performance. In extensive simulations, we demonstrate that such an approach reliably recovers true covariates under diverse noise scenarios and improves both selection accuracy and stability. We then apply the proposed method to a forestry data set, analyzing the distribution of trees in relation to elevation and soil nutrients in a tropical rain forest. This shows the practical utility of the method, which provides a systematic framework for robust variable selection in spatial point-process models under noise, without requiring additional knowledge of the process.

Problem

• Robust variable selection for spatial point processes with noisy observations
• Addressing noise-induced spurious displacements and missed event detections
• Identifying influential spatial covariates under diverse noise scenarios

Innovation

• Stability selection with point-process subsampling for robustness
• Non-convex best-subset penalty enhances model selection
• Sparsity-promoting estimation recovers true covariates under noise