Related papers: Spectral estimation of Hawkes processes from count…
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…
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 Whittle likelihood is a widely used and computationally efficient pseudo-likelihood. However, it is known to produce biased parameter estimates for large classes of models. We propose a method for de-biasing Whittle estimates for…
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…
In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a nonparametric estimator of the…
In this paper, we present a maximum likelihood method for estimating the parameters of a univariate Hawkes process with self-excitation or inhibition. Our work generalizes techniques and results that were restricted to the self-exciting…
Extracting the spectral representations of the neural processes that underlie spiking activity is key to understanding how the brain rhythms mediate cognitive functions. While spectral estimation of continuous time-series is well studied,…
Many modern spatio-temporal data sets, in sociology, epidemiology or seismology, for example, exhibit self-exciting characteristics, triggering and clustering behaviors both at the same time, that a suitable Hawkes space-time process can…
Hawkes processes are a popular framework to model the occurrence of sequential events, i.e., occurrence dynamics, in several fields such as social diffusion. In real-world scenarios, the inter-arrival time among events is irregular.…
We have established a sparse estimation method for the generalized exponential marked Hawkes process by the penalized method to the ordinary method (P-O) estimator. Furthermore, we evaluated the probability of correct variable selection. In…
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 often applied to model dependence and interaction phenomena in multivariate event data sets, such as neuronal spike trains, social interactions, and financial transactions. In the nonparametric setting, learning the…
We adopt the interpretability offered by a parametric, Hawkes-process-inspired conditional probability mass function for the marks and apply variational inference techniques to derive a general and scalable inferential framework for marked…
It is often assumed that events cannot occur simultaneously when modelling data with point processes. This raises a problem as real-world data often contains synchronous observations due to aggregation or rounding, resulting from…
The Whittle likelihood is widely used for Bayesian nonparametric estimation of the spectral density of stationary time series. However, the loss of efficiency for non-Gaussian time series can be substantial. On the other hand, parametric…
We present a modified version of the non parametric Hawkes kernel estimation procedure studied in arXiv:1401.0903 that is adapted to slowly decreasing kernels. We show on numerical simulations involving a reasonable number of events that…
Hawkes Processes are a type of point process for modeling self-excitation, i.e., when the occurrence of an event makes future events more likely to occur. The corresponding self-triggering function of this type of process may be inferred…
We prove that the number of points of a stationary linear Hawkes process lying in any bounded subset of the real line has exponential moments, without any other assumption than the one needed for existence of such stationary process, namely…
This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…
We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each nodes of the process, but also disentangles the…