Related papers: A Multidimensional Fractional Hawkes Process for M…
Human behavior drives a range of complex social, urban, and economic systems, yet understanding its structure and dynamics at the individual level remains an open question. From credit card transactions to communications data, human…
Hawkes processes are a class of point processes that have the ability to model the self- and mutual-exciting phenomena. Although the classic Hawkes processes cover a wide range of applications, their expressive ability is limited due to…
Sequences of events including infectious disease outbreaks, social network activities, and crimes are ubiquitous and the data on such events carry essential information about the underlying diffusion processes between communities (e.g.,…
Existing spatio-temporal Hawkes process models typically rely on either parametric or semiparametric assumptions, limiting the model's ability to capture complex endogenous and exogenous event dynamics. We propose a fully Bayesian…
The Hawkes process is a widely used model in many areas, such as finance, seismology, neuroscience, epidemiology, and social sciences. Estimation of the Hawkes process from continuous observations of a sample path is relatively…
Earthquake occurrence is notoriously difficult to predict. While some aspects of their spatiotemporal statistics can be relatively well captured by point-process models, very little is known regarding the magnitude of future events, and it…
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…
We investigate the spatial distribution of aftershocks and we find that aftershock linear density exhibits a maximum, that depends on the mainshock magnitude, followed by a power law decay. The exponent controlling the asymptotic decay and…
Modeling seismic activity rates and clustering plays an important role in studies of induced seismicity associated with mining and other resource extraction operations. This is critical for understanding the physical and statistical…
Multivariate Hawkes Processes (MHPs) are a class of point processes that can account for complex temporal dynamics among event sequences. In this work, we study the accuracy and computational efficiency of three classes of algorithms which,…
We introduce and establish the main properties of QHawkes ("Quadratic" Hawkes) models. QHawkes models generalize the Hawkes price models introduced in E. Bacry et al. (2014), by allowing all feedback effects in the jump intensity that are…
A key difficulty that arises from real event data is imprecision in the recording of event time-stamps. In many cases, retaining event times with a high precision is expensive due to the sheer volume of activity. Combined with practical…
The field of study of complex systems holds that the dynamics of complex systems are founded on universal principles that may used to describe a great variety of scientific and technological approaches of different types of natural,…
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…
In this paper we study the frequentist properties of Bayesian approaches in linear high dimensional Hawkes processes in a sparse regime where the number of interaction functions acting on each component of the Hawkes process is much smaller…
In this paper, we propose an extension of the Hawkes process by incorporating a kernel based on the tempered Mittag-Leffler distribution. This is the generalization of the work presented in [10]. We derive analytical results for the…
We propose a novel approach to marked Hawkes kernel inference which we name the moment-based neural Hawkes estimation method. Hawkes processes are fully characterized by their first and second order statistics through a Fredholm integral…
We present an analytical solution and numerical tests of the epidemic-type aftershock (ETAS) model for aftershocks, which describes foreshocks, aftershocks and mainshocks on the same footing. The occurrence rate of aftershocks triggered by…
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.…
The productivity of a magnitude $m$ event can be characterized in term of triggered events of magnitude above $m-\Delta$: it is the number of direct "descendants" $\nu_\Delta$ and the number of all "descendants" $V_\Delta$. There is…