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Hawkes process is a class of simple point processes with self-exciting and clustering properties. Hawkes process has been widely applied in finance, neuroscience, social networks, criminology, seismology, and many other fields. In this…
Social media conversations unfold based on complex interactions between users, topics and time. While recent models have been proposed to capture network strengths between users, users' topical preferences and temporal patterns between…
Aggressive behavior in autistic inpatient youth often arises in temporally clustered bursts complicating efforts to distinguish external triggers from internal escalation. The sample population branching factor-the expected number of new…
Networks and temporal point processes serve as fundamental building blocks for modeling complex dynamic relational data in various domains. We propose the latent space Hawkes (LSH) model, a novel generative model for continuous-time…
Events in spatiotemporal domains arise in numerous real-world applications, where uncovering event relationships and enabling accurate prediction are central challenges. Classical Poisson and Hawkes processes rely on restrictive parametric…
Quadratic Hawkes (QHawkes) processes have proved effective at reproducing the statistics of price changes, capturing many of the stylised facts of financial markets. Motivated by the recently reported strong occurrence of endogenous…
We analyze the probability density function (PDF) of waiting times between financial loss exceedances. The empirical PDFs are fitted with the self-excited Hawkes conditional Poisson process with a long power law memory kernel. The Hawkes…
Previous work has shown that popular trending events are important external factors which pose significant influence on user search behavior and also provided a way to computationally model this influence. However, their problem formulation…
A Hawkes process model with a time-varying background rate is developed for analyzing the high-frequency financial data. In our model, the logarithm of the background rate is modeled by a linear model with a relatively large number of…
This study investigates and uses multi-kernel Hawkes models to describe a high-frequency mid-price process. Each kernel represents a different responsive speed of market participants. Using the conditional Hessian, we examine whether the…
We study the spatio-temporal prediction problem, which has attracted the attention of many researchers due to its critical real-life applications. In particular, we introduce a novel approach to this problem. Our approach is based on the…
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…
We present a careful analysis of possible issues on the application of the self-excited Hawkes process to high-frequency financial data. We carefully analyze a set of effects leading to significant biases in the estimation of the…
While the presence of clustering in crime and security event data is well established, the mechanism(s) by which clustering arises is not fully understood. Both contagion models and history independent correlation models are applied, but…
Some recent papers relate the criticality of complex systems to their maximal capacity of information processing. In the present paper, we consider high dimensional point processes, known as age-dependent Hawkes processes, which have been…
We derive exact analytical expressions for the cumulants of any orders of neuronal membrane potentials driven by spike trains in a multivariate Hawkes process model with excitation and inhibition. Such expressions can be used for the…
Classic estimation methods for Hawkes processes rely on the assumption that observed event times are indeed a realisation of a Hawkes process, without considering any potential perturbation of the model. However, in practice, observations…
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,…
Crowdfunding is a powerful tool for individuals or organizations seeking financial support from a vast audience. Despite widespread adoption, managers often lack information about dynamics of their platforms. Hawkes processes have been used…
In this paper we consider multivariate Hawkes processes with baseline hazard and kernel functions that depend on time. This defines a class of locally stationary processes. We discuss estimation of the time-dependent baseline hazard and…