Related papers: Linear prediction of point process times and marks
Point processes are widely used statistical models for continuous-time discrete event data, such as medical records, crime reports, and social network interactions, to capture the influence of historical events on future occurrences. In…
Hawkes processes are a class of point processes that have the ability to model the self- and mutual-exciting phenomena. Although the classic Hawkes processes cover a wide range of applications, their expressive ability is limited due to…
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…
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…
In this paper we consider point processes specified on directed linear networks, i.e. linear networks with associated directions. We adapt the so-called conditional intensity function used for specifying point processes on the time line to…
Spatio-temporal Hawkes point processes are a particularly interesting class of stochastic point processes for modeling self-exciting behavior, in which the occurrence of one event increases the probability of other events occurring. These…
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…
The Wiener-Hopf equations are a Toeplitz system of linear equations that naturally arise in several applications in time series. These include the update and prediction step of the stationary Kalman filter equations and the prediction of…
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…
We show that the jumps correlation matrix of a multivariate Hawkes process is related to the Hawkes kernel matrix through a system of Wiener-Hopf integral equations. A Wiener-Hopf argument allows one to prove that this system (in which the…
This paper presents a parametric estimation method for ill-observed linear stationary Hawkes processes. When the exact locations of points are not observed, but only counts over time intervals of fixed size, methods based on the likelihood…
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…
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…
A temporal point process is a stochastic process that predicts which type of events is likely to happen and when the event will occur given a history of a sequence of events. There are various examples of occurrence dynamics in the daily…
Detecting rare events, those defined to give rise to high impact but have a low probability of occurring, is a challenge in a number of domains including meteorological, environmental, financial and economic. The use of machine learning to…
We propose a novel modeling framework for time-evolving networks allowing for long-term dependence in network features that update in continuous time. Dynamic network growth is functionally parameterized via the conditional intensity of a…
The Hawkes process has become a standard method for modeling self-exciting event sequences with different event types. A recent work has generalized the Hawkes process to a neurally self-modulating multivariate point process, which enables…
The Hawkes process is a simple point process with wide applications in finance, social networks, criminology, seismology, and many other fields. The Hawkes process is defined for continuous-time setting. However, data is also recorded in a…
Asynchronous events on the continuous time domain, e.g., social media actions and stock transactions, occur frequently in the world. The ability to recognize occurrence patterns of event sequences is crucial to predict which typeof events…
An extension of the Hawkes process, the Marked Hawkes process distinguishes itself by featuring variable jump size across each event, in contrast to the constant jump size observed in a Hawkes process without marks. While extensive…