Related papers: Age Dependent Hawkes Process
Over the past few decades, the Hawkes process has become a popular framework for modeling temporal events thanks to its flexibility to capture different dependency structures. The objective of this work is to model call sequences emitted by…
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…
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…
Asynchronous events sequences are widely distributed in the natural world and human activities, such as earthquakes records, users activities in social media and so on. How to distill the information from these seemingly disorganized data…
We consider the learning of multi-agent Hawkes processes, a model containing multiple Hawkes processes with shared endogenous impact functions and different exogenous intensities. In the framework of stochastic maximum likelihood…
In this work we introduce two variants of multivariate Hawkes models with an explicit dependency on various queue sizes aimed at modeling the stochastic time evolution of a limit order book. The models we propose thus integrate 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 Hawkes process is a simple point process, whose intensity function depends on the entire past history and is self-exciting and has the clustering property. The Hawkes process is in general non-Markovian. The linear Hawkes process has…
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…
The self-exciting Hawkes process is widely used to model events which occur in bursts. However, many real world data sets contain missing events and/or noisily observed event times, which we refer to as data distortion. The presence of such…
Cognitive ageing seems to be a story of global degradation. As one ages there are a number of physical, chemical and biological changes that take place. Therefore it is logical to assume that the brain is no exception to this phenomenon.…
We study statistical aspects of state-dependent Hawkes processes, which are an extension of Hawkes processes where a self- and cross-exciting counting process and a state process are fully coupled, interacting with each other. The…
We report on both analytical and numerical results concerning stochastic Hopfield--like neural automata exhibiting the following (biologically inspired) features: (1) Neurons and synapses evolve in time as in contact with respective baths…
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…
To overcome some limits of classical neuronal models, we propose a Markovian generalization of the classical model based on Jacobi processes by introducing downwards jumps to describe the activity of a single neuron. The statistical…
We prove regenerative properties for the linear Hawkes process under minimal assumptions on the transfer function, which may have unbounded support. These results are applicable to sliding window statistical estimators. We exploit…
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…
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…
This paper introduces the Neural Network for Nonlinear Hawkes processes (NNNH), a non-parametric method based on neural networks to fit nonlinear Hawkes processes. Our method is suitable for analyzing large datasets in which events exhibit…
The Hawkes process and its extensions effectively model self-excitatory phenomena including earthquakes, viral pandemics, financial transactions, neural spike trains and the spread of memes through social networks. The usefulness of these…