Related papers: High dimensional Hawkes processes
We propose a novel probabilistic framework to model continuous-time interaction events data. Our goal is to infer the \emph{implicit} community structure underlying the temporal interactions among entities, and also to exploit how the…
Existence and stability properties are studied for Hawkes process, i.e. point process $S$ that has long-memory and intensity $r(t)=\lambda \big(g_0(t)+ \sum_{\tau<t, \tau \in S} h(t-\tau) \big)$. The approach to Hawkes process presented in…
This paper focuses on limit theorems for linear Hawkes processes with random marks. We prove a large deviation principle, which answers the question raised by Bordenave and Torrisi. A central limit theorem is also obtained. We conclude with…
Learning the latent network structure from large scale multivariate point process data is an important task in a wide range of scientific and business applications. For instance, we might wish to estimate the neuronal functional…
Neural computations arising from myriads of interactions between spiking neurons can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this…
Many phenomena can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this difficulty, the Poisson Hypothesis regime replaces interaction…
Hawkes processes have recently gained increasing attention from the machine learning community for their versatility in modeling event sequence data. While they have a rich history going back decades, some of their properties, such as…
We consider a multivariate non-linear Hawkes process in a multi-class setup where particles are organised within two populations of possibly different sizes, such that one of the populations acts excitatory on the system while the other…
Classic results show that the Hawkes self-exciting point process can be viewed as a collection of temporal clusters, where exogenously generated initial events give rise to endogenously driven descendant events. This perspective provides…
Classic estimation methods for Hawkes processes rely on the assumption that observed event times are indeed a realisation of a Hawkes process, without considering any potential perturbation of the model. However, in practice, observations…
In this paper, we investigate the asymptotic behavior of nearly unstable Hawkes processes whose regression kernel has $L^1$ norm strictly greater than one and close to one as time goes to infinity. We find that,the scaling size determines…
The Hawkes process is a model for counting the number of arrivals to a system which exhibits the self-exciting property - that one arrival creates a heightened chance of further arrivals in the near future. The model, and its…
We consider a system of $N$ Hawkes processes and observe the actions of a subpopulation of size $K \le N$ up to time $t$, where $K$ is large. The influence relationships between each pair of individuals are modeled by i.i.d.Bernoulli($p$)…
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…
We propose a mean-field model of interacting point processes where each process has a memory of the time elapsed since its last event (age) and its recent past (leaky memory), generalizing Age-dependent Hawkes processes. The model is…
We prove exponential moments for linear combinations of the number of individuals of each type of a whole multitype Poissonian Galton Watson process. We give sharp estimates for such quantities, which depend on the expectation of the…
Many networks have event-driven dynamics (such as communication, social media and criminal networks), where the mean rate of the events occurring at a node in the network changes according to the occurrence of other events in the network.…
The propagation of chaos and associated law of large numbers for mean-field interacting age-dependent Hawkes processes (when the number of processes n goes to +$\infty$) being granted by the study performed in (Chevallier, 2015), the aim of…
Stochastic processes play a key role for modeling a huge variety of transport problems out of equilibrium, with manifold applications throughout the natural and social sciences. To formulate models of stochastic dynamics the conventional…
Consider an N-dimensional Markov chain obtained from N one-dimensional random walks by Doob h-transform with the q-Vandermonde determinant. We prove that as N becomes large, these Markov chains converge to an infinite-dimensional Feller…