Spatio-temporal Point Process Research Articles

Transformer-based neural marked spatio temporal point process model for analyzing football match events

Predictive modeling plays a crucial role in machine learning, data analysis, and statistics. In sports, predictive modeling methods have emerged to provide insights and evaluate performances based on key performance metrics. However, most existing models tend to focus on predicting only partial aspects of an event, such as the outcome, action type, or location, while neglecting the temporal factors involved. To address this gap, this study introduces the Transformer-Based Neural Marked Spatio-Temporal Point Process (NMSTPP) model, specifically designed for football event data. The NMSTPP model predicts a comprehensive set of future event components, including inter-event time, zone, and action. Additionally, it features a dependent prediction layers architecture to enhance model performance. The Holistic Possession Utilization Score (HPUS) metric is also proposed to evaluate the effectiveness and efficiency of possession periods in football based on the NMSTPP model. With open-source football event data, the NMSTPP model successfully predicted the aforementioned three components of future events, with an improvement of up to 4% overall and 9% for individual components compared to baseline models. The HPUS demonstrated a 0.9 correlation with existing performance metrics, highlighting its utility in performance evaluation. The NMSTPP and HPUS were applied to the Premier League to demonstrate their practical feasibility.

Multivariate Hawkes Spatio-Temporal Point Process with attention for point of interest recommendation

Multivariate Hawkes Spatio-Temporal Point Process with attention for point of interest recommendation

Crime risk assessment through Cox and self-exciting spatio-temporal point processes

Crime risk assessment through Cox and self-exciting spatio-temporal point processes

Predicting urban signal-controlled intersection congestion events using spatio-temporal neural point process

ABSTRACT The urban traffic signal-controlled intersections are of great significance for solving the problem of urban road congestion. Previous research on congestion prediction mainly aggregated data at the level of road segments or traffic flow at a coarse regulated time interval. Fine-grained prediction of congestion events at the lane-level and cycle-level enables detailed a understanding of spatio-temporal dependencies, leading to congestion reduction, improved efficiency. This paper presents a Spatio-Temporal Neural Point Process (STNPP) model that combines Graph Neural Networks and Neural Temporal Point Process to predict congestion events at urban intersections. The proposed model allows for complete prediction of congestion events, including their occurrence, development, dissipation. In the process of spatial correlation modeling, graph neural networks are used to model the spatial relationships between both region and intersections. The current intersection and its upstream/downstream areas are modeled separately. To model the temporal correlations at individual intersections, we focus on a specific lane and capture the evolution of congestion events using the Neural Point Process Gated Recurrent Unit (NPPGRU), which captures the temporal granularity changes of signal-controlled cycles in congestion events. Using actual traffic speed and signal-controlled data from Hangzhou city, we validate that the proposed method achieves stable predictive performance.

Convolutional Non-Homogeneous Poisson Process and its Application to Wildfire Ignition Risk Quantification for Power Delivery Networks

To quantify wildfire ignition risks on power delivery networks, the current practice predominantly relies on the empirically calculated fire danger indices, which may not well capture the effects of dynamically changing environmental factors. This article proposes a spatio-temporal point process model, known as the Convolutional Non-homogeneous Poisson Process (cNHPP), and applies the model to quantify wildfire ignition risks for power delivery networks. The proposed model captures both the current (i.e., instantaneous) and cumulative (i.e., historical) effects of key environmental processes (i.e., covariates) on wildfire risks, as well as the spatio-temporal dependency among different segments of the power delivery network. The computation and interpretation of the intensity function are thoroughly investigated. We apply the proposed approach to estimate wildfire ignition risks on major transmission lines in California, using historical fire data, meteorological and vegetation data obtained from the National Oceanic and Atmospheric Administration and National Aeronautics and Space Administration. A comprehensive comparison study is performed to show the applicability and predictive capability of the proposed approach.

Nonparametric second-order estimation for spatiotemporal point patterns.

Many existing methodologies for analyzing spatiotemporal point patterns are developed based on the assumption of stationarity in both space and time for the second-order intensity or pair correlation. In practice, however, such an assumption often lacks validity or proves to be unrealistic. In this paper, we propose a novel and flexible nonparametric approach for estimating the second-order characteristics of spatiotemporal point processes, accommodating non-stationary temporal correlations. Our proposed method employs kernel smoothing and effectively accounts for spatial and temporal correlations differently. Under a spatially increasing-domain asymptotic framework, we establish consistency of the proposed estimators, which can be constructed using different first-order intensity estimators to enhance practicality. Simulation results reveal that our method, in comparison with existing approaches, significantly improves statistical efficiency. An application to a COVID-19 dataset further illustrates the flexibility and interpretability of our procedure.

Unveiling Multi-Agent Strategies: A Data-Driven Approach for Extracting and Evaluating Team Tactics from Football Event and Freeze-Frame Data

Studying collective behavior in opposing multi-agent teams is crucial across game theory, robotics, and sports analytics. In sports, especially football, team tactics involve intricate strategic spatial and action behaviors displayed as event sequences during possession. Understanding and analyzing these tactics is essential for successful training, strategic planning, and on-field success. While traditional approaches, such as notational and statistical analyses, offer valuable insights into team tactics, they often lack a comprehensive consideration of contextual information, thereby limiting the holistic evaluation of teams’ performances. To bridge this gap and capture the nuanced intricacies of team tactics, we employed advanced methodologies. The sequential pattern mining algorithm PrefixSpan was utilized to extract tactical patterns from possession sequences, enabling a deeper understanding of how teams strategize and adapt during play. Additionally, the neural marked spatio temporal point process (NMSTPP) model was leveraged to model and predict team behaviors, facilitating a fair comparison among teams. The evaluation of team possessions was further enhanced through the innovative holistic possession utilization score metrics, providing a more nuanced assessment of performance. In our experimental exploration, we identified and classified five distinct team tactics, validated the efficacy of the NMSTPP model when integrating StatsBomb 360 data, and conducted a comprehensive analysis of English Premier League teams during the 2022/2023 season. The results were visualized using radar plots and scatter plots with mean shift clustering. Lastly, the potential applications to RoboCup were discussed.

Summary statistics for spatio-temporal point processes on linear networks

We propose novel second/higher-order summary statistics for inhomogeneous spatio-temporal point processes when the spatial locations are limited to a linear network. More specifically, letting the spatial distance between events be measured by a regular distance metric, appropriate forms of K- and J-functions are introduced, and their theoretical relationships are studied. The theoretical forms of our proposed summary statistics are investigated under homogeneity, Poissonness, and independent thinning. Moreover, non-parametric estimators are derived, facilitating the use of our proposed summary statistics to study the spatio-temporal dependence between events. Through simulation studies, we demonstrate that our proposed J-function effectively identifies spatio-temporal clustering, inhibition, and randomness. Finally, we examine spatio-temporal dependencies for street crimes in Valencia, Spain, and traffic accidents in New York, USA.

Spatio-Temporal Marked Point Process Model to Understand Forest Fires in the Mediterranean Basin

AbstractUnderstanding and predicting forest fires have proved a highly difficult endeavour, which requires extending and adapting complex models used in different fields. Here, we apply a marked point process approach, commonly used in ecology, which uses multiple Gaussian random fields to represent dynamics of Mediterranean forest fires in a spatio-temporal distribution model. Inference is carried out using Integrated Nested Laplace Approximation (INLA) with , an accessible and computationally efficient approach for Bayesian hierarchical modelling, which is not yet widely used in species distribution models. Using the marked point process approach, intensity of forest fires and dispersion were predicted using socioeconomic factors and environmental and fire-related variables. This demonstrates the advantage of complex model components in accounting for spatio-temporal dynamics that are not explained by environmental variables. Introduction of spatio-temporal marked point process can provide a more realistic perspective of a system, which is of particular importance for a practical and impact-focused worldwide problem such as forest fires.Supplementary materials accompanying this paper appear online.

Minimum contrast for the first-order intensity estimation of spatial and spatio-temporal point processes

In this paper, we harness a result in point process theory, specifically the expectation of the weighted K-function, where the weighting is done by the true first-order intensity function. This theoretical result can be employed as an estimation method to derive parameter estimates for a particular model assumed for the data. The underlying motivation is to avoid the difficulties associated with dealing with complex likelihoods in point process models and their maximization. The exploited result makes our method theoretically applicable to any model specification. In this paper, we restrict our study to Poisson models, whose likelihood represents the base for many more complex point process models. In this context, our proposed method can estimate the vector of local parameters that correspond to the points within the analyzed point pattern without introducing any additional complexity compared to the global estimation. We illustrate the method through simulation studies for both purely spatial and spatio-temporal point processes and show complex scenarios based on the Poisson model through the analysis of two real datasets concerning environmental problems.

Severe convective storms’ reproduction: empirical analysis from the marked self-exciting point processes point of view

The paper focuses on the evaluation of hailstorms’ and thunderstorms winds’ events in the United States of America, in the period from 1996 to 2022, under the marked spatio-temporal self-exciting point processes point of view. The aim of the present article is the assessment and description of the spatio-temporal spontaneous and reproducing activity of severe hailstorms’ and thunderstorms winds’ processes. The present application shows how the spatio-temporal pattern is well-fitted and clearly explainable, according to the flexible semi-parametric ETAS model fitting.

Stelfi: An R package for fitting Hawkes and log-Gaussian Cox point process models.

Modelling spatial and temporal patterns in ecology is imperative to understand the complex processes inherent in ecological phenomena. Log-Gaussian Cox processes are a popular choice among ecologists to describe the spatiotemporal distribution of point-referenced data. In addition, point pattern models where events instigate others nearby (i.e., self-exciting behaviour) are becoming increasingly popular to infer the contagious nature of events (e.g., animal sightings). While there are existing R packages that facilitate fitting spatiotemporal point processes and, separately, self-exciting models, none incorporate both. We present an R package, stelfi, that fits spatiotemporal self-exciting and log-Gaussian Cox process models using Template Model Builder through a range of custom-written C++ templates. We illustrate the use of stelfi's functions fitting models to Sasquatch (bigfoot) sightings data within the USA. The structure of these data is typical of many seen in ecology studies. We show, from a temporal Hawkes process to a spatiotemporal self-exciting model, how the models offered by the package enable additional insights into the temporal and spatial progression of point pattern data. We present extensions to these well-known models that include spatiotemporal self-excitation and joint likelihood models, which are better suited to capture the complex mechanisms inherent in many ecological data. The package stelfi offers user-friendly functionality, is open source, and is available from CRAN. It offers the implementation of complex spatiotemporal point process models in R for applications even beyond the field of ecology.

Spatio-temporal point process intensity estimation using zero-deflated subsampling applied to a lightning strikes dataset in France

Spatio-temporal point process intensity estimation using zero-deflated subsampling applied to a lightning strikes dataset in France

A Bayesian Inference Method for a Large Magnitude Event in a Spatiotemporal Marked Point Process Representing Seismic Activity

A Bayesian Inference Method for a Large Magnitude Event in a Spatiotemporal Marked Point Process Representing Seismic Activity

Authors’ reply to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’

Authors’ reply to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’

A spatio-temporal analysis of fire occurrence patterns in the Brazilian Amazon

Wildfires in the Amazon significantly impact the forest structure and carbon cycle. Understanding the patterns of fire occurrence is crucial for effective management. A novel spatio-temporal point process framework was used to analyze changes in fire occurrence patterns in the Brazilian Amazon. A dynamic representation of a Log Gaussian Cox process was used to model the intensity function, which was decomposed into trend, seasonality, cycles, covariates, and spatial effects. The results show a marked decrease in long-term fire occurrence movements between the start of the sample and 2012, followed by an increase until the end of the sample, attributed to governance measures and market mechanisms. Spatial variability of fire occurrence rates in the Brazilian Amazon was successfully captured, with regions having more dry seasons experiencing higher fire occurrence rates. This analysis provides valuable insights into fire occurrence patterns in the Amazon region and the factors driving them.

A neural encoder for earthquake rate forecasting

Forecasting the timing of earthquakes is a long-standing challenge. Moreover, it is still debated how to formulate this problem in a useful manner, or to compare the predictive power of different models. Here, we develop a versatile neural encoder of earthquake catalogs, and apply it to the fundamental problem of earthquake rate prediction, in the spatio-temporal point process framework. The epidemic type aftershock sequence model (ETAS) effectively learns a small number of parameters to constrain the assumed functional forms for the space and time correlations of earthquake sequences (e.g., Omori-Utsu law). Here we introduce learned spatial and temporal embeddings for point process earthquake forecasting models that capture complex correlation structures. We demonstrate the generality of this neural representation as compared with ETAS model using train-test data splits and how it enables the incorporation additional geophysical information. In rate prediction tasks, the generalized model shows >4% improvement in information gain per earthquake and the simultaneous learning of anisotropic spatial structures analogous to fault traces. The trained network can be also used to perform short-term prediction tasks, showing similar improvement while providing a 1000-fold reduction in run-time.

Proposer of the vote of thanks to Narayanan, Kosmidis and Dellaportas and contribution to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’

Proposer of the vote of thanks to Narayanan, Kosmidis and Dellaportas and contribution to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’

Seconder of the vote of thanks to Narayanan, Kosmidis, and Dellaportas and contribution to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’

Seconder of the vote of thanks to Narayanan, Kosmidis, and Dellaportas and contribution to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’

Ron Yurko and Rebecca Nugent’s contribution to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’ by Narayanan, Kosmidis, and Dellaportas

Ron Yurko and Rebecca Nugent’s contribution to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’ by Narayanan, Kosmidis, and Dellaportas