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Related papers: Conditional Uniformity and Hawkes Processes

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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…

Methodology · Statistics 2022-12-26 Rui Zhang , Haoyun Wang , Yao Xie

In this paper, we study a discrete-time analogue of a Hawkes process, modelled as a Poisson autoregressive process whose parameters depend on the past of the trajectory. The model is characterized to allow these parameters to take negative…

Probability · Mathematics 2024-09-04 Manon Costa , Pascal Maillard , Anthony Muraro

We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate…

Machine Learning · Computer Science 2016-09-23 Young Lee , Kar Wai Lim , Cheng Soon Ong

Event occurrence is not only subject to the environmental changes, but is also facilitated by the events that have occurred in a system. Here, we develop a method for estimating such extrinsic and intrinsic factors from a single series of…

Data Analysis, Statistics and Probability · Physics 2021-01-04 Shinsuke Koyama , Shigeru Shinomoto

We present the first exact analysis of some of the temporal properties of multivariate self-excited Hawkes conditional Poisson processes, which constitute powerful representations of a large variety of systems with bursty events, for which…

Statistical Mechanics · Physics 2014-08-26 A. Saichev , D. Sornette

Hawkes processes are a class of self-exciting point processes that are used to model complex phenomena. While most applications of Hawkes processes assume that event data occurs in continuous-time, the less-studied discrete-time version of…

Applications · Statistics 2023-06-01 Trinnhallen Brisley , Gordon Ross , Daniel Paulin , Jake Easto

We develop a Bayesian nonparametric framework for inference in spatio-temporal Hawkes processes, extending existing theoretical results beyond the purely temporal setting. Our framework encompasses modelling both the background and…

Statistics Theory · Mathematics 2026-01-08 Xenia Miscouridou , Deborah Sulem

We generalise the construction of multivariate Hawkes processes to a possibly infinite network of counting processes on a directed graph $\mathbb G$. The process is constructed as the solution to a system of Poisson driven stochastic…

Probability · Mathematics 2014-03-25 Sylvain Delattre , Nicolas Fournier , Marc Hoffmann

Hawkes process is a class of simple point processes with self-exciting and clustering properties. Hawkes process has been widely applied in finance, neuroscience, social networks, criminology, seismology, and many other fields. In this…

Probability · Mathematics 2020-11-23 Fuqing Gao , Lingjiong Zhu

The Hawkes process has garnered attention in recent years for its suitability to describe the behavior of online information cascades. Here, we present a fully tractable approach to analytically describe the distribution of the number of…

Physics and Society · Physics 2020-07-22 Joseph D. O'Brien , Alberto Aleta , Yamir Moreno , James P. Gleeson

This paper considers population processes in which general, not necessarily Markovian, multivariate Hawkes processes dictate the stochastic arrivals. We establish results to determine the corresponding time-dependent joint probability…

Probability · Mathematics 2021-06-08 Raviar Karim , Roger J. A. Laeven , Michel Mandjes

We introduce, and formally establish, a variant of the Hawkes-fed birth-death process -- the delayed Hawkes birth-death process -- in which the conditional intensity does not increase at arrivals but at departures from the system. In a…

Probability · Mathematics 2025-07-24 Justin Baars , Roger J. A. Laeven , Michel Mandjes

Hawkes process is a simple point process that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applications in finance, neuroscience, social networks,…

Probability · Mathematics 2018-10-02 Xuefeng Gao , Lingjiong Zhu

Learning causal structure among event types on multi-type event sequences is an important but challenging task. Existing methods, such as the Multivariate Hawkes processes, mostly assumed that each sequence is independent and identically…

Machine Learning · Computer Science 2022-05-17 Ruichu Cai , Siyu Wu , Jie Qiao , Zhifeng Hao , Keli Zhang , Xi Zhang

Let $F$ be a distribution function on $\mathbb{R}$ with $F(0) = 0 $ and density $f$. Let $\tilde{F}$ be the distribution function of $X_1 - X_2$, $X_i\sim F,\, i=1,2,\text{ iid}$. We show that for a critical Hawkes process with displacement…

Probability · Mathematics 2017-06-14 Matthias Kirchner

Event history data from sports competitions have recently drawn increasing attention in sports analytics to generate data-driven strategies. Such data often exhibit self-excitation in the event occurrence and dependence within event…

Methodology · Statistics 2026-01-14 K. Ken Peng , X. Joan Hu , Tim B. Swartz

Given a collection of entities (or nodes) in a network and our intermittent observations of activities from each entity, an important problem is to learn the hidden edges depicting directional relationships among these entities. Here, we…

Machine Learning · Statistics 2017-08-01 Triet M Le

We propose a novel framework for modeling multiple multivariate point processes, each with heterogeneous event types that share an underlying space and obey the same generative mechanism. Focusing on Hawkes processes and their variants that…

Machine Learning · Computer Science 2021-02-05 Hongteng Xu , Dixin Luo , Hongyuan Zha

Marked Temporal Point Processes (MTPPs) arise naturally in medical, social, commercial, and financial domains. However, existing Transformer-based methods mostly inject temporal information only via positional encodings, relying on shared…

Machine Learning · Computer Science 2026-03-25 Xinzi Tan , Kejian Zhang , Junhan Yu , Doudou Zhou

We examine a distributional fixed-point equation related to a multi-type branching process that is key in the cluster sizes analysis of multivariate heavy-tailed Hawkes processes. Specifically, we explore the tail behavior of its solution…

Probability · Mathematics 2025-04-07 Jose Blanchet , Roger J. A. Laeven , Xingyu Wang , Bert Zwart