Related papers: A Mutually Exciting Latent Space Hawkes Process Mo…
The evolution of communities in dynamic (time-varying) network data is a prominent topic of interest. A popular approach to understanding these dynamic networks is to embed the dyadic relations into a latent metric space. While methods for…
From social networks to Internet applications, a wide variety of electronic communication tools are producing streams of graph data; where the nodes represent users and the edges represent the contacts between them over time. This has led…
The Hawkes process, a self-exciting point process, has a wide range of applications in modeling earthquakes, social networks and stock markets. The established estimation process requires that researchers have access to the exact time…
Hawkes processes are a class of self-exciting point processes that are used to model complex phenomena. While most applications of Hawkes processes assume that event data occurs in continuous-time, the less-studied discrete-time version of…
This paper presents a stochastic model motivated by the study of a virus-like evolving population with different mutation rates. This is a continuous time birth-death model: the birth processes are mutually-exciting Hawkes processes and the…
This chapter provides an accessible introduction for point processes, and especially Hawkes processes, for modeling discrete, inter-dependent events over continuous time. We start by reviewing the definitions and the key concepts in point…
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…
We introduce a nonlinear modification of the classical Hawkes process, which allows inhibitory couplings between units without restrictions. The resulting system of interacting point processes provides a useful mathematical model 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.…
Network data are often sampled with auxiliary information or collected through the observation of a complex system over time, leading to multiple network snapshots indexed by a continuous variable. Many methods in statistical network…
The large volumes of data generated by human activities such as online purchases, health records, spatial mobility etc. are stored as a sequence of events over a continuous time. Learning deep learning methods over such sequences is a…
Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to…
Reconstructing full spatio-temporal dynamics from sparse observations in both space and time remains a central challenge in complex systems, as measurements can be spatially incomplete and can be also limited to narrow temporal windows. Yet…
In this chapter, we show how to efficiently model high-dimensional extreme peaks-over-threshold events over space in complex non-stationary settings, using extended latent Gaussian Models (LGMs), and how to exploit the fitted model in…
The superposition of temporal point processes has been studied for many years, although the usefulness of such models for practical applications has not be fully developed. We investigate superposed Hawkes process as an important class of…
Modern network data analysis often involves analyzing network structures alongside covariate features to gain deeper insights into underlying patterns. However, traditional covariate-assisted statistical network models may not adequately…
Dynamics of interacting systems in engineering, society, and nature often evolve over latent networks that govern which entities can interact. We study the problem of inferring these networks from event-based observations, which arise…
Data similarity (or distance) computation is a fundamental research topic which fosters a variety of similarity-based machine learning and data mining applications. In big data analytics, it is impractical to compute the exact similarity of…
In this paper, we build a model for biological neural nets where the activity of the network is described by Hawkes processes having a variable length memory. The particularity of this paper is to deal with an infinite number of components.…
Targeting a better understanding of credit market dynamics, the authors have studied a stochastic model named the Hawkes process. Describing trades arrival times, this kind of model allows for the capture of self-excitement and mutual…