Related papers: Multiplicatively interacting point processes and a…
Nonlinear dynamics of spiking neural networks has recently attracted much interest as an approach to understand possible information processing in the brain and apply it to artificial intelligence. Since information can be processed by…
We consider a nonlinear multivariate Hawkes process having a variable length memory which allows to describe the activity of a neuronal network by its membrane potential. We propose a graphical construction of the process and we construct,…
The relative timing of action potentials in neurons recorded from local cortical networks often shows a non-trivial dependence, which is then quantified by cross-correlation functions. Theoretical models emphasize that such spike train…
Understanding the diffusion in social network is an important task. However, this task is challenging since (1) the network structure is usually hidden with only observations of events like "post" or "repost" associated with each node, and…
Generalized evolutionary point processes offer a class of point process models that allows for either excitation or inhibition based upon the history of the process. In this regard, we propose modeling which comprises generalization of the…
Link prediction models are increasingly used to recommend interactions in evolving networks, yet their impact on network structure is typically assessed from static snapshots. In particular, observed homophily conflates intrinsic…
We present a stability study of the class of multivariate self-excited Hawkes point processes, that can model natural and social systems, including earthquakes, epileptic seizures and the dynamics of neuron assemblies, bursts of exchanges…
Neural spike trains, which are sequences of very brief jumps in voltage across the cell membrane, were one of the motivating applications for the development of point process methodology. Early work required the assumption of stationarity,…
Multivariate Hawkes processes are a widely used class of self-exciting point processes, but maximum likelihood estimation naively scales as $O(N^2)$ in the number of events. The canonical linear exponential Hawkes process admits a faster…
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…
Networks of interconnected neurons communicating through spiking signals offer the bedrock of neural computations. Our brains spiking neural networks have the computational capacity to achieve complex pattern recognition and cognitive…
We address the questions of identifying pairs of interacting neurons from the observation of their spiking activity. The neuronal network is modeled by a system of interacting point processes with memory of variable length. The influence of…
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…
Hawkes process is a simple point process that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applications in finance, neuroscience, social networks,…
In this work, we study the event occurrences of individuals interacting in a network. To characterize the dynamic interactions among the individuals, we propose a group network Hawkes process (GNHP) model whose network structure is observed…
Spatio-temporal Hawkes point processes are a particularly interesting class of stochastic point processes for modeling self-exciting behavior, in which the occurrence of one event increases the probability of other events occurring. These…
Network data often take the form of repeated interactions between senders and receivers tabulated over time. A primary question to ask of such data is which traits and behaviors are predictive of interaction. To answer this question, a…
The spike trains are the main components of the information processing in the brain. To model spike trains several point processes have been investigated in the literature. And more macroscopic approaches have also been studied, using…
We introduce a new supervised learning algorithm based to train spiking neural networks for classification. The algorithm overcomes a limitation of existing multi-spike learning methods: it solves the problem of interference between…
The Hawkes process (HP) is commonly used to model event sequences with self-reinforcing dynamics, including electronic health records (EHRs). Traditional HPs capture self-reinforcement via parametric impact functions that can be inspected…