Related papers: Statistical Inference for Networks of High-Dimensi…
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…
This paper proposes a new meta-learning method -- named HARMLESS (HAwkes Relational Meta LEarning method for Short Sequences) for learning heterogeneous point process models from short event sequence data along with a relational network.…
The Hawkes process is a popular point process model for event sequences that exhibit temporal clustering. The intensity process of a Hawkes process consists of two components, the baseline intensity and the accumulated excitation effect due…
We establish the asymptotic validity of frequency-domain inference for stationary multivariate Hawkes processes under mild conditions, bridging the gap between theory and application. By developing upper-bounds on the reduced cumulant…
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…
Traditionally, Hawkes processes are used to model time--continuous point processes with history dependence. Here we propose an extended model where the self--effects are of both excitatory and inhibitory type and follow a Gaussian Process.…
Learning the influence structure of multiple time series data is of great interest to many disciplines. This paper studies the problem of recovering the causal structure in network of multivariate linear Hawkes processes. In such processes,…
We characterize a Hawkes point process with kernel proportional to the probability density function of Mittag-Leffler random variables. This kernel decays as a power law with exponent $\beta +1 \in (1,2]$. Several analytical results can be…
We investigate applications of deep neural networks to a point process having an intensity with mixing covariates processes as input. Our generic model includes Cox-type models and marked point processes as well as multivariate point…
Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…
We study a multivariate Hawkes process as a model for time-continuous relational event networks. The model does not assume the network to be known, it includes covariates, and it allows for both common drivers, parameters common to all 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…
Foundational marked temporal point process (MTPP) models, such as the Hawkes process, often use inexpressive model families in order to offer interpretable parameterizations of event data. On the other hand, neural MTPPs models forego this…
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 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…
This study proposes a novel method for estimation and hypothesis testing in high-dimensional single-index models. We address a common scenario where the sample size and the dimension of regression coefficients are large and comparable.…
As a tool for capturing irregular temporal dependencies (rather than resorting to binning temporal observations to construct time series), Hawkes processes with exponential decay have seen widespread adoption across many application…
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…
Modelling and forecasting the occurrence of extreme events is especially difficult when the event process is nonstationary, with changes in both the rate at which extremes occur and the magnitude of the extremes when they occur. We approach…
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…