Related papers: Age Dependent Hawkes Process
The Hawks process is a point process with a self-exciting property. It has been used to model earthquakes, social media events, infections, etc., and is getting a lot of attention. However, as a real problem, there are often situations…
New cells are generated throughout life and integrate into the hippocampus via the process of adult neurogenesis. Epileptogenic brain injury induces many structural changes in the hippocampus, including the death of interneurons and altered…
Topological data analysis (TDA) approaches are becoming increasingly popular for studying the dependence patterns in multivariate time series data. In particular, various dependence patterns in brain networks may be linked to specific tasks…
Temporal networks allow representing connections between objects while incorporating the temporal dimension. While static network models can capture unchanging topological regularities, they often fail to model the effects associated with…
In this paper, we analyze status update systems modeled through the Stochastic Hybrid Systems (SHSs) tool. Contrary to previous works, we allow the system's transition dynamics to be polynomial functions of the Age of Information (AoI).…
Recent studies have shown how spiking networks can learn complex functionality through error-correcting plasticity, but the resulting structures and dynamics remain poorly studied. To elucidate how these models may link to observed dynamics…
Online learning of Hawkes processes has received increasing attention in the last couple of years especially for modeling a network of actors. However, these works typically either model the rich interaction between the events or the latent…
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…
Mobile health applications, including those that track activities such as exercise, sleep, and diet, are becoming widely used. Accurately predicting human actions is essential for targeted recommendations that could improve our health and…
We show that the jumps correlation matrix of a multivariate Hawkes process is related to the Hawkes kernel matrix through a system of Wiener-Hopf integral equations. A Wiener-Hopf argument allows one to prove that this system (in which the…
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…
We propose a statistical model of a large random network with high connectivity in order to describe the behavior of {\it E.\,coli} cells after exposure to acute stress. The building blocks of this network are feedback cycles typical of the…
Dynamical criticality has been shown to enhance information processing in dynamical systems, and there is evidence for self-organized criticality in neural networks. A plausible mechanism for such self-organization is activity dependent…
Adult neurogenesis has long been documented in the vertebrate brain, and recently even in humans. Although it has been conjectured for many years that its functional role is related to the renewing of memories, no clear mechanism as to how…
In this paper, we are interested in linear prediction of a particular kind of stochastic process, namely a marked temporal point process. The observations are event times recorded on the real line, with marks attached to each event. We show…
Consider observing a collection of discrete events within a network that reflect how network nodes influence one another. Such data are common in spike trains recorded from biological neural networks, interactions within a social network,…
Spiking activity of neurons engaged in learning and performing a task show complex spatiotemporal dynamics. While the output of recurrent network models can learn to perform various tasks, the possible range of recurrent dynamics that…
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…
The order flow in high-frequency financial markets has been of particular research interest in recent years, as it provides insights into trading and order execution strategies and leads to better understanding of the supply-demand…
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…