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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…

Social and Information Networks · Computer Science 2018-11-16 Baichuan Yuan , Hao Li , Andrea L. Bertozzi , P. Jeffrey Brantingham , Mason A. Porter

In this work, we propose to catch the complexity of the membrane potential's dynamic of a motoneuron between its spikes, taking into account the spikes from other neurons around. Our approach relies on two types of data: extracellular…

Statistics Theory · Mathematics 2021-08-03 Anna Bonnet , Charlotte Dion , François Gindraud , Sarah Lemler

Cascading chains of events are a salient feature of many real-world social, biological, and financial networks. In social networks, social reciprocity accounts for retaliations in gang interactions, proxy wars in nation-state conflicts, or…

Machine Learning · Statistics 2016-07-05 Eric C. Hall , Rebecca M. Willett

Human activities generate various event sequences such as taxi trip records, bike-sharing pick-ups, crime occurrence, and infectious disease transmission. The point process is widely used in many applications to predict such events related…

Machine Learning · Computer Science 2024-01-30 Yoshiaki Takimoto , Yusuke Tanaka , Tomoharu Iwata , Maya Okawa , Hideaki Kim , Hiroyuki Toda , Takeshi Kurashima

The Hawkes self-excited point process provides an efficient representation of the bursty intermittent dynamics of many physical, biological, geological and economic systems. By expressing the probability for the next event per unit time…

Statistical Mechanics · Physics 2020-09-23 Kiyoshi Kanazawa , Didier Sornette

Point processes have been dominant in modeling the evolution of seismicity for decades, with the Epidemic Type Aftershock Sequence (ETAS) model being most popular. Recent advances in machine learning have constructed highly flexible point…

Geophysics · Physics 2023-10-04 Samuel Stockman , Daniel J. Lawson , Maximilian J. Werner

The multivariate Hawkes process (MHP) is widely used for analyzing data streams that interact with each other, where events generate new events within their own dimension (via self-excitation) or across different dimensions (via…

Machine Learning · Computer Science 2024-11-01 Pio Calderon , Alexander Soen , Marian-Andrei Rizoiu

The Hawkes process is a self-exciting sample point process. It has wide applications in finance, social networks, criminology, seismology, and many other fields. With the development of storage technology, data-driven models are attracting…

Probability · Mathematics 2021-06-23 Haixu Wang

The Hawkes process is a simple point process that has long memory, clustering effect, self-exciting property and is in general non-Markovian. The future evolution of a self-exciting point process is influenced by the timing of the past…

Probability · Mathematics 2013-06-25 Lingjiong Zhu

Abstract. Most of the real world data we encounter are asynchronous event sequence, so the last decades have been characterized by the implementation of various point process into the field of social networks,electronic medical records and…

Machine Learning · Computer Science 2021-12-28 Zhi-yan Song , Jian-wei Liu , Lu-ning Zhang , Ya-nan Han

A new general procedure for a priori selection of more predictable events from a time series of observed variable is proposed. The procedure is applicable to time series which contains different types of events that feature significantly…

Neural and Evolutionary Computing · Computer Science 2007-05-23 Igor B. Konovalov

Point process models are widely used for continuous asynchronous event data, where each data point includes time and additional information called "marks", which can be locations, nodes, or event types. This paper presents a novel point…

Machine Learning · Statistics 2024-11-12 Zheng Dong , Matthew Repasky , Xiuyuan Cheng , Yao Xie

Foundational marked temporal point process (MTPP) models, such as the Hawkes process, often use inexpressive model families in order to offer interpretable parameterizations of event data. On the other hand, neural MTPPs models forego this…

Machine Learning · Statistics 2025-11-04 Alex Boyd , Andrew Warrington , Taha Kass-Hout , Parminder Bhatia , Danica Xiao

Self-exciting spatio-temporal point process models predict the rate of events as a function of space, time, and the previous history of events. These models naturally capture triggering and clustering behavior, and have been widely used in…

Methodology · Statistics 2018-08-14 Alex Reinhart

Forecasting earthquake sequences remains a central challenge in seismology, particularly under non-stationary conditions. While deep learning models have shown promise, their ability to generalize across time remains poorly understood. We…

The Hawks process is a point process with a self-exciting property. It has been used to model earthquakes, social media events, infections, etc., and is getting a lot of attention. However, as a real problem, there are often situations…

Statistics Theory · Mathematics 2021-07-30 Masatoshi Goda

Temporal networks allow representing connections between objects while incorporating the temporal dimension. While static network models can capture unchanging topological regularities, they often fail to model the effects associated with…

Machine Learning · Computer Science 2025-07-11 Mathilde Perez , Raphaël Romero , Bo Kang , Tijl De Bie , Jefrey Lijffijt , Charlotte Laclau

Spatiotemporal point processes (STPPs) are probabilistic models for events occurring in continuous space and time. Real-world event data often exhibit intricate dependencies and heterogeneous dynamics. By incorporating modern deep learning…

Machine Learning · Computer Science 2025-02-14 Sumantrak Mukherjee , Mouad Elhamdi , George Mohler , David A. Selby , Yao Xie , Sebastian Vollmer , Gerrit Grossmann

Hawkes processes are a particularly interesting class of stochastic process that have been applied in diverse areas, from earthquake modelling to financial analysis. They are point processes whose defining characteristic is that they…

Probability · Mathematics 2015-07-13 Patrick J. Laub , Thomas Taimre , Philip K. Pollett

Networks and temporal point processes serve as fundamental building blocks for modeling complex dynamic relational data in various domains. We propose the latent space Hawkes (LSH) model, a novel generative model for continuous-time…

Machine Learning · Computer Science 2022-07-08 Zhipeng Huang , Hadeel Soliman , Subhadeep Paul , Kevin S. Xu