Related papers: Multiplicatively interacting point processes and a…
Nonlinear systems driven by recurrent signals are known to exhibit complex dynamical responses which, in the physiological context, can have important functional consequences. One of the simplest biological systems that is exposed to such…
Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…
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…
Simultaneous recordings from multiple neural units allow us to investigate the activity of very large neural ensembles. To understand how large ensembles of neurons process sensory information, it is necessary to develop suitable…
This work focuses on a self-exciting point process defined by a Hawkes-like intensity and a switching mechanism based on a hidden Markov chain. Previous works in such a setting assume constant intensities between consecutive events. We…
Stochastic processes with long memories, known as long memory processes, are ubiquitous in various science and engineering problems. Superposing Markovian stochastic processes generates a non-Markovian long memory process serving as…
Point processes are a useful mathematical tool for describing events over time, and so there are many recent approaches for representing and learning them. One notable open question is how to precisely describe the flexibility of point…
The characterization of network and biophysical properties from neural spiking activity is an important goal in neuroscience. A framework that provides unbiased inference on causal synaptic interaction and single neural properties has been…
A new class of models for dynamic networks is proposed, called mutually exciting point process graphs (MEG). MEG is a scalable network-wide statistical model for point processes with dyadic marks, which can be used for anomaly detection…
For a class of excitatory spiking neuron models with delayed feedback fed with a Poisson stochastic process, it is proven that the stream of output interspike intervals cannot be presented as a Markov process of any order. Keywords: spiking…
We consider a population of Hawkes processes modeling the activity of $N$ interacting neurons. The neurons are regularly positioned on the circle $[-\pi, \pi]$, and the connectivity between neurons is given by a cosine kernel. The firing…
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…
Hawkes processes are a self-exciting stochastic process used to describe phenomena whereby past events increase the probability of the occurrence of future events. This work presents a flexible approach for modelling a variant of these,…
We present a new CUSUM procedure for sequentially detecting change-point in the self and mutual exciting processes, a.k.a. Hawkes networks using discrete events data. Hawkes networks have become a popular model for statistics and machine…
Optogenetics is a new tool to study neuronal circuits that have been genetically modified to allow stimulation by flashes of light. We study recordings from single neurons within neural circuits under optogenetic stimulation. The data from…
When inhibitory neurons constitute about 40% of neurons they could have an important antinociceptive role, as they would easily regulate the level of activity of other neurons. We consider a simple network of cortical spiking neurons with…
Group-based social dominance hierarchies are of essential interest in animal behavior research. Studies often record aggressive interactions observed over time, and models that can capture such dynamic hierarchy are therefore crucial.…
We analyse the stochastic comparison of interacting particle systems allowing for multiple arrivals, departures and non-conservative jumps of individuals between sites. That is, if $k$ individuals leave site $x$ for site $y$, a possibly…
The study of interacting dynamical systems continues to attract research interest in various fields of science and engineering. In a collection of interacting particles, the interaction network contains information about how various…
Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…