We investigate spatio-temporal event analysis using point processes. Inferring the dynamics of event sequences spatiotemporally has many practical applications including crime prediction, social media analysis, and traffic forecasting. In particular, we focus on spatio-temporal Hawkes processes that are commonly used due to their capability to capture excitations between event occurrences. We introduce a novel inference framework based on randomized transformations and gradient descent to learn the process. We replace the spatial kernel calculations by randomized Fourier feature-based transformations. The introduced randomization by this representation provides flexibility while modeling the spatial excitation between events. Moreover, the system described by the process is expressed within closed-form in terms of scalable matrix operations. During the optimization, we use maximum likelihood estimation approach and gradient descent while properly handling positivity and orthonormality constraints. The experiment results show the improvements achieved by the introduced method in terms of fitting capability in synthetic and real datasets with respect to the conventional inference methods in the spatio-temporal Hawkes process literature. We also analyze the triggering interactions between event types and how their dynamics change in space and time through the interpretation of learned parameters.
Yale University（耶鲁大学）；Princeton University（普林斯顿大学）；Georgia Institute of Technology（佐治亚理工学院）
We estimate the general influence functions for spatio-temporal Hawkes processes using a tensor recovery approach by formulating the location dependent influence function that captures the influence of historical events as a tensor kernel. We assume a low-rank structure for the tensor kernel and cast the estimation problem as a convex optimization problem using the Fourier transformed nuclear norm (TNN). We provide theoretical performance guarantees for our approach and present an algorithm to solve the optimization problem. Moreover, we demonstrate the efficiency of our estimation with numeri…
Imperial College London（伦敦帝国理工学院）；University of Copenhagen（哥本哈根大学）；Boston College（波士顿学院）；University of Oxford（牛津大学）
Hawkes processes are point process models that have been used to capture self-excitatory behavior in social interactions, neural activity, earthquakes and viral epidemics. They can model the occurrence of the times and locations of events. Here we develop a new class of spatiotemporal Hawkes processes that can capture both triggering and clustering behavior and we provide an efficient method for performing inference. We use a log-Gaussian Cox process (LGCP) as prior for the background rate of the Hawkes process which gives arbitrary flexibility to capture a wide range of underlying background …
Hawkes process is one of the most commonly used models for investigating the self-exciting nature of earthquake occurrences. However, seismicity patterns have complicated characteristics due to heterogeneous geology and stresses, for which existing methods with Hawkes process cannot fully capture. This study introduces novel nonparametric Hawkes process models that are flexible in three distinct ways. First, we incorporate the spatial inhomogeneity of the self-excitation earthquake productivity. Second, we consider the anisotropy in aftershock occurrences. Third, we reflect the space-time inte…
Indiana University - Purdue University Indianapolis（印第安纳大学-普渡大学印第安纳波利斯分校）
We propose a novel framework for integrating Hawkes processes with multi-armed bandit algorithms to solve spatio-temporal event forecasting and detection problems when data may be undersampled or spatially biased. In particular, we introduce an upper confidence bound algorithm using Bayesian spatial Hawkes process estimation for balancing the tradeoff between exploiting geographic regions where data has been collected and exploring geographic regions where data is unobserved. We first validate our model using simulated data and then apply it to the problem of disaster search and rescue using c…
There is often latent network structure in spatial and temporal data and the tools of network analysis can yield fascinating insights into such data. In this paper, we develop a nonparametric method for network reconstruction from spatiotemporal data sets using multivariate Hawkes processes. In contrast to prior work on network reconstruction with point-process models, which has often focused on exclusively temporal information, our approach uses both temporal and spatial information and does not assume a specific parametric form of network dynamics. This leads to an effective way of recoverin…
Duke University School of Medicine（杜克大学医学院）；Duke University（杜克大学）；InfiniaML, Inc.（InfiniaML公司）
Health risks from cigarette smoking -- the leading cause of preventable death in the United States -- can be substantially reduced by quitting. Although most smokers are motivated to quit, the majority of quit attempts fail. A number of studies have explored the role of self-reported symptoms, physiologic measurements, and environmental context on smoking risk, but less work has focused on the temporal dynamics of smoking events, including daily patterns and related nicotine effects. In this work, we examine these dynamics and improve risk prediction by modeling smoking as a self-triggering pr…
A multivariate Hawkes process enables self- and cross-excitations through a triggering matrix that behaves like an asymmetrical covariance structure, characterizing pairwise interactions between the event types. Full-rank estimation of all interactions is often infeasible in empirical settings. Models that specialize on a spatiotemporal application alleviate this obstacle by exploiting spatial locality, allowing the dyadic relationships between events to depend only on separation in time and relative distances in real Euclidean space. Here we generalize this framework to any multivariate Hawke…
We study the spatio-temporal prediction problem, which has attracted the attention of many researchers due to its critical real-life applications. In particular, we introduce a novel approach to this problem. Our approach is based on the Hawkes process, which is a non-stationary and self-exciting point process. We extend the formulations of a standard point process model that can represent time-series data to represent a spatio-temporal data. We model the data as nonstationary in time and space. Furthermore, we partition the spatial region we are working on into subregions via an adaptive deci…
Graphon Hawkes Processes: Sparse Estimation and Network Recovery
University of Amsterdam（阿姆斯特丹大学）；Eurandom, Eindhoven University of Technology（埃因霍温理工大学 Eurandom）；CentER, Tilburg University（蒂尔堡大学 CentER）；Mathematical Institute, Leiden University（莱顿大学数学研究所）；Korteweg-de Vries Institute for Mathematics, University of Amsterdam（阿姆斯特丹大学柯特韦格-德弗里斯数学研究所）；Amsterdam Business School, University of Amsterdam（阿姆斯特丹大学阿姆斯特丹商学院）
Mutations sometimes increase contagiousness for evolving pathogens. During an epidemic, scientists use viral genome data to infer a shared evolutionary history and connect this history to geographic spread. We propose a model that directly relates a pathogen's evolution to its spatial contagion dynamics -- effectively combining the two epidemiological paradigms of phylogenetic inference and self-exciting process modeling -- and apply this \emph{phylogenetic Hawkes process} to a Bayesian analysis of 23,422 viral cases from the 2014-2016 Ebola outbreak in West Africa. The proposed model is able …
Crimes emerge out of complex interactions of human behaviors and situations. Linkages between crime incidents are highly complex. Detecting crime linkage given a set of incidents is a highly challenging task since we only have limited information, including text descriptions, incident times, and locations. In practice, there are very few labels. We propose a new statistical modeling framework for {\it spatio-temporal-textual} data and demonstrate its usage on crime linkage detection. We capture linkages of crime incidents via multivariate marked spatio-temporal Hawkes processes and treat embed…
A self-exciting spatio-temporal point process is fitted to incident data from the UK National Traffic Information Service to model the rates of primary and secondary accidents on the M25 motorway in a 12-month period during 2017-18. This process uses a background component to represent primary accidents, and a self-exciting component to represent secondary accidents. The background consists of periodic daily and weekly components, a spatial component and a long-term trend. The self-exciting components are decaying, unidirectional functions of space and time. These components are determined via…
Predicting discrete events in time and space has many scientific applications, such as predicting hazardous earthquakes and outbreaks of infectious diseases. History-dependent spatio-temporal Hawkes processes are often used to mathematically model these point events. However, previous approaches have faced numerous challenges, particularly when attempting to forecast one or multiple future events. In this work, we propose a new neural architecture for simultaneous multi-event forecasting of spatio-temporal point processes, utilizing transformers, augmented with normalizing flows and probabilis…
We consider online monitoring of the network event data to detect local changes in a cluster when the affected data stream distribution shifts from one point process to another with different parameters. Specifically, we are interested in detecting a change point that causes a shift of the underlying data distribution that follows a multivariate Hawkes process with exponential decay temporal kernel, whereby the Hawkes process is considered to account for spatio-temporal correlation between observations. The proposed detection procedure is based on scan score statistics. We derive the asymptoti…
Georgia Institute of Technology（佐治亚理工学院）；Duke University（杜克大学）
Self- and mutually-exciting point processes are popular models in machine learning and statistics for dependent discrete event data. To date, most existing models assume stationary kernels (including the classical Hawkes processes) and simple parametric models. Modern applications with complex event data require more general point process models that can incorporate contextual information of the events, called marks, besides the temporal and location information. Moreover, such applications often require non-stationary models to capture more complex spatio-temporal dependence. To tackle these …
This article proposes a spatiotemporal point process model that enhances the classical Epidemic-Type Aftershock Sequence (ETAS) model by incorporating a renewal main-shock arrival process, which we term the renewal ETAS (RETAS) model. This modification is similar in spirit to the renewal Hawkes (RHawkes) process but the conditional intensity process supports a spatial domain. It empowers the main-shock intensity with the capability to reset upon the arrival of main-shocks and therefore allows for heavier clustering of earthquakes than the spatiotemporal ETAS model introduced by Ogata (1998). W…
We develop a new family of marked point processes by focusing the characteristic properties of marked Hawkes processes exclusively to the space of marks, providing the freedom to specify a different model for the occurrence times. This is possible through the decomposition of the joint distribution of marks and times that allows to separately specify the conditional distribution of marks given the filtration of the process and the current time. We develop a Bayesian framework for the inference and prediction from this family of marked point processes that can naturally accommodate process and …
Robust Wave Origin Detection from Sensor Array Data via Randomized Hough Transform and Model Fitting
Aberdeen Institute of Data Science and Artificial Intelligence, South China Normal University（华南师范大学阿伯丁数据科学与人工智能研究所）；Department of Statistics and Data Science, The Chinese University of Hong Kong（香港中文大学统计与数据科学系）
Indian Institute of Technology Hyderabad（印度理工学院海得拉巴分校）；TCS Research（塔塔咨询服务研究部）
Event data consisting of time of occurrence of the events arises in several real-world applications. Recent works have introduced neural network based point processes for modeling event-times, and were shown to provide state-of-the-art performance in predicting event-times. However, neural point process models lack a good uncertainty quantification capability on predictions. A proper uncertainty quantification over event modeling will help in better decision making for many practical applications. Therefore, we propose a novel point process model, Bayesian Neural Hawkes process (BNHP) which le…
Seahorse: A Unified Benchmarking Framework for Spatiotemporal Event Modeling
German Research Center for Artificial Intelligence (DFKI), Data Science and its Applications Research Group, Kaiserslautern, Germany（德国人工智能研究中心（DFKI），数据科学及其应用研究组，凯泽斯劳滕，德国）；Department of Computer Science, Rhineland-Palatinate Technical University of Kaiserslautern-Landau (RPTU), Kaiserslautern, Germany（计算机科学系，莱茵兰-普法尔茨凯泽斯劳滕-兰道工业大学（RPTU），凯泽斯劳滕，德国）
Stanford University（斯坦福大学）；University of Minnesota（明尼苏达大学）；Center for Magnetic Resonance Research（磁共振研究中心）；University of Minnesota Medical School（明尼苏达大学医学院）
Magnetic resonance imaging (MRI) nowadays serves as an important modality for diagnostic and therapeutic guidance in clinics. However, the {\it slow acquisition} process, the dynamic deformation of organs, as well as the need for {\it real-time} reconstruction, pose major challenges toward obtaining artifact-free images. To cope with these challenges, the present paper advocates a novel subspace learning framework that permeates benefits from parallel factor (PARAFAC) decomposition of tensors (multiway data) to low-rank modeling of temporal sequence of images. Treating images as multiway data …
Learning to Factorize and Adapt: A Versatile Approach Toward Universal Spatio-Temporal Foundation Models
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；Peking University（北京大学）；Huawei 2012 Laboratories（华为2012实验室）；East China Normal University（华东师范大学）
