Related papers: Hawkes processes with variable length memory and a…
Event-scheduling algorithms can compute in continuous time the next occurrence of points (as events) of a counting process based on their current conditional intensity. In particular event-scheduling algorithms can be adapted to perform the…
We consider a population of Hawkes processes modeling the activity of $N$ interacting neurons. The neurons are regularly positioned on the segment $[0,1]$, and the connectivity between neurons is given by a random possibly diluted and…
The multivariate Hawkes process is a past-dependent point process used to model the relationship of event occurrences between different phenomena.Although the Hawkes process was originally introduced to describe excitation effects, which…
We consider the problem of learning the network of mutual excitations (i.e., the dependency graph) in a non-stationary, multivariate Hawkes process. We consider a general setting where baseline rates at each node are time-varying and delay…
We consider multi-class systems of interacting nonlinear Hawkes processes modeling several large families of neurons and study their mean field limits. As the total number of neurons goes to infinity we prove that the evolution within each…
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…
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…
The event sequence of many diverse systems is represented as a sequence of discrete events in a continuous space. Examples of such an event sequence are earthquake aftershock events, financial transactions, e-commerce transactions, social…
Networks capture our intuition about relationships in the world. They describe the friendships between Facebook users, interactions in financial markets, and synapses connecting neurons in the brain. These networks are richly structured…
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…
We consider a new class of interacting particle systems with a countable number of interacting components. The system represents the time evolution of the membrane potentials of an infinite set of interacting neurons. We prove the existence…
We introduce the Hyperedge-triggered Hawkes (HTH) process for inferring higher-order interaction structure in multi-cellular systems from asynchronous event-time data. Beyond standard pairwise excitation, the HTH intensity includes a term…
We propose a simulation method for multidimensional Hawkes processes based on superposition theory of point processes. This formulation allows us to design efficient simulations for Hawkes processes with differing exponentially decaying…
Multivariate Hawkes process provides a powerful framework for modeling temporal dependencies and event-driven interactions in complex systems. While existing methods primarily focus on uncovering causal structures among observed…
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…
Some recent papers relate the criticality of complex systems to their maximal capacity of information processing. In the present paper, we consider high dimensional point processes, known as age-dependent Hawkes processes, which have been…
Hawkes Processes are a type of point process which models self-excitement among time events. It has been used in a myriad of applications, ranging from finance and earthquakes to crime rates and social network activity analysis.Recently, a…
Multivariate point processes are widely applied to model event-type data such as natural disasters, online message exchanges, financial transactions or neuronal spike trains. One very popular point process model in which the probability of…
In this work, we study the event occurrences of individuals interacting in a network. To characterize the dynamic interactions among the individuals, we propose a group network Hawkes process (GNHP) model whose network structure is observed…
In the last decade Hawkes processes have received much attention as models for functional connectivity in neural spiking networks and other dynamical systems with a cascade behavior. In this paper we establish a renewal approach for…