model point processes

This paper addresses the challenge of modeling population-level variability in replicated point processes. We propose a novel functional principal component analysis (fPCA) framework grounded in random measures and the cumulative mass function (CMF). Introducing the concept of “principal measures,” we establish the Karhunen–Loève expansion for random measures and derive a Mercer-type theorem for their covariance measures, enabling consistent parameter-rate estimation of eigencomponents. The method integrates fPCA, random measure theory, and nonparametric/semiparametric estimation, yielding closed-form solutions for Poisson and Hawkes processes. Evaluated on seismological, single-cell spatial transcriptomic, and neurophysiological datasets, our approach significantly improves both the accuracy of identifying population-level variation structures in point patterns and their biological interpretability.

Traditional models struggle to characterize nonstationary spatial point processes—e.g., those exhibiting intensity discontinuities, hotspots, or spatial heterogeneity. To address this, we propose a Cox process model based on stochastic spatial partitioning. Our method employs a partitioned Gaussian process prior to explicitly capture intensity discontinuities and local variations; integrates a random segmentation mechanism with infinite-dimensional MCMC sampling to avoid grid-based discretization, thereby preserving nonparametric flexibility while substantially reducing computational cost; and incorporates spatial covariates to elucidate underlying drivers of intensity variation. Experiments on synthetic and real-world datasets demonstrate that the approach achieves high-fidelity inference of nonstationary intensity structures, robustly identifies change-point boundaries and hotspot regions, and provides a scalable, interpretable nonparametric Bayesian framework for complex spatial point patterns.

This work proposes a nonparametric spatiotemporal point process model based on Gaussian processes to overcome the limitations of traditional approaches, which often rely on restrictive parametric assumptions or lack interpretability in capturing complex event dependencies. The model employs a separable kernel and a structured grid to separately represent the background intensity and the triggering influence kernel, thereby achieving both flexibility and interpretability. To enhance scalability, the method leverages a Kronecker-structured covariance matrix and tensor-product Gauss–Legendre quadrature, enabling efficient handling of large-scale spatiotemporal event data. Experimental results demonstrate that the proposed approach significantly outperforms existing models across multiple real-world datasets, offering superior predictive accuracy and computational efficiency.

This study addresses the challenge of modeling dynamic excitation effects in event-time data under repeated external stimuli. The authors propose a Hierarchical Excitation Process (HEP), which represents the conditional intensity as a superposition of time-evolving dynamic kernel functions and incorporates a hierarchical structure to yield interpretable modulation of stimulus responses. By integrating likelihood-based point process inference with model-driven clustering, the method simultaneously captures individual response dynamics and identifies latent subpopulations exhibiting similar excitation patterns. Experimental results demonstrate that HEP accurately recovers the underlying dynamic latent structure in synthetic data and effectively reveals time-varying neuronal excitability across different experimental conditions in spike train recordings from the abdominal ganglion of Aplysia.

To address computational inefficiency and limited representational capacity arising from explicit intensity function modeling in high-dimensional marked temporal point processes, this paper proposes an intensity-free implicit conditional generative framework. Methodologically, we pioneer the integration of implicit generative modeling into marked point processes, designing an end-to-end differentiable architecture that jointly encodes event timestamps, types, and high-dimensional marks (e.g., text, images), leveraging conditional GANs and sequence encoders for history-driven, high-fidelity future event generation. Our core contribution lies in eliminating reliance on parametric intensity functions, thereby significantly enhancing dynamic modeling capability and sampling efficiency. Extensive experiments on multiple real-world high-dimensional datasets demonstrate that our approach outperforms state-of-the-art methods in both event generation quality and prediction accuracy, while accelerating training by over 3×.

This study addresses the challenge of disentangling background spatial inhomogeneity—driven by site-specific attractiveness—from inter-individual repulsive interactions in pedestrian waiting behavior, using repeated observations of spatial point patterns. To this end, the authors propose a novel semi-parametric spatial point process model that integrates a determinantal point process with a Gibbs point process. For the first time, repeated spatial point patterns are incorporated into the inference framework of such models, enabling parameter estimation and model assessment based on multiple independent and identically distributed spatial realizations. Applied to real-world pedestrian waiting scenarios, the method successfully reproduces key empirical spatial characteristics, demonstrating its effectiveness in capturing complex crowd distributions and achieving a tight integration of methodological innovation with practical application.

This study addresses causal inference for continuous spatiotemporal point processes subject to spillover and lingering effects under unit-level interventions. It proposes the first causal inference framework grounded in the potential outcomes paradigm, modeling the observed post-intervention process as an unlabeled superposition of control and treated components. Identification is achieved by separately analyzing regions within and outside the support of the intervention, leveraging a structured point process model to recover causal contrasts in non-support areas. Estimation employs a likelihood-based stochastic EM algorithm, augmented with a predictable block-wise hard EM surrogate, making it applicable to history-dependent processes such as Poisson and Hawkes processes. The method provides non-asymptotic error bounds and plug-in inference guarantees. Empirical validation on wastewater injection and seismicity data from Oklahoma demonstrates its practical efficacy.

This work addresses the lack of reliable and reproducible comparisons among existing neural spatiotemporal point process (STPP) models, which stems from inconsistent preprocessing, coordinate normalization, data partitioning, and evaluation protocols. To remedy this, we propose SEAHORSE, a unified benchmarking framework that enables fair training, tuning, and evaluation of diverse neural STPP models through a standardized encode-evolve-decode architecture, likelihood computation in raw coordinates, and consistent evaluation protocols. We further introduce HawkesNest, a novel synthetic stress-test suite that systematically reveals the inductive biases of different models under complex event patterns. Experiments demonstrate that model performance is highly sensitive to the complexity of event dynamics: some methods degrade sharply while others remain robust, underscoring the critical value of our benchmark for analyzing model robustness.

This study addresses the challenges in modeling global and local effects within inhomogeneous pairwise interaction Gibbs point processes and the lack of effective methods for testing complete spatial randomness (CSR). To overcome these limitations, the authors propose a hierarchical Bayesian framework that, for the first time, integrates basis function expansions with Bayesian hierarchical modeling to flexibly characterize both the intensity and interaction functions. Building on posterior inference, they develop a Bayesian testing procedure specifically designed for CSR assessment. The approach enables efficient inference via Markov chain Monte Carlo (MCMC) and demonstrates strong empirical performance: when applied to water strider distribution and forest fire data, it successfully uncovers complex spatial dependence structures and provides reliable CSR tests, substantially enhancing the flexibility and inferential power of Gibbs point process modeling.

Existing spatiotemporal Hawkes process models often rely on parametric or semi-parametric assumptions, limiting their ability to flexibly capture complex dynamics between endogenous and exogenous events. This work proposes the first Bayesian nonparametric spatiotemporal Hawkes process model based on additive Gaussian processes, which decouples the spatiotemporal background intensity from the triggering kernel. This design enhances interpretability while preserving high flexibility and enabling principled uncertainty quantification. Leveraging sparse variational inference with a Gaussian variational family, the model achieves efficient and scalable learning. Experiments demonstrate that the method accurately recovers background and triggering structures on synthetic data, attains higher leave-one-out log-likelihood on real-world datasets, and reveals interpretable self-exciting spatiotemporal patterns.