Related papers: Graphical Modeling for Multivariate Hawkes Process…
Modern health care systems are conducting continuous, automated surveillance of the electronic medical record (EMR) to identify adverse events with increasing frequency; however, many events such as sepsis do not have elucidated prodromes…
Event-driven systems in fields such as neuroscience, social networks, and finance often exhibit dynamics influenced by continuously evolving external covariates. Motivated by these applications, we introduce a new class of multivariate…
Learning the causal-interaction network of multivariate Hawkes processes is a useful task in many applications. Maximum-likelihood estimation is the most common approach to solve the problem in the presence of long observation sequences.…
In this paper, we design a nonparametric online algorithm for estimating the triggering functions of multivariate Hawkes processes. Unlike parametric estimation, where evolutionary dynamics can be exploited for fast computation of the…
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…
Point process modeling is gaining increasing attention, as point process type data are emerging in numerous scientific applications. In this article, motivated by a neuronal spike trains study, we propose a novel point process regression…
The Hawkes process is a simple point process that has long memory, clustering effect, self-exciting property and is in general non-Markovian. The future evolution of a self-exciting point process is influenced by the timing of the past…
Both Hawkes processes and autoregressive processes rely on linear functionals of their past, while modeling different types of data. Since datasets arising from observations of the same phenomenon may be heterogeneous and sampled at…
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…
Multi-electrode neurophysiological recordings produce massive quantities of data. Multivariate time series analysis provides the basic framework for analyzing the patterns of neural interactions in these data. It has long been recognized…
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…
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…
Learning causal structure among event types from discrete-time event sequences is a particularly important but challenging task. Existing methods, such as the multivariate Hawkes processes based methods, mostly boil down to learning the…
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…
Recently proposed encoder-decoder structures for modeling Hawkes processes use transformer-inspired architectures, which encode the history of events via embeddings and self-attention mechanisms. These models deliver better prediction and…
Multi-dimensional Hawkes process (MHP) is a class of self and mutually exciting point processes that find wide range of applications -- from prediction of earthquakes to modelling of order books in high frequency trading. This paper makes…
The description of the dynamics of complex systems, in particular the capture of the interaction structure and causal relationships between elements of the system, is one of the central questions of interdisciplinary research. While the…
We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series…
Causality is crucial to understanding the mechanisms behind complex systems and making decisions that lead to intended outcomes. Event sequence data is widely collected from many real-world processes, such as electronic health records, web…
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…