Related papers: An Empirical Study of Continuous Connectivity Degr…
We study the analogue of Poisson ensembles of Markov loops ('loop soups') in the setting of one-dimensional diffusions. We give a detailed description of the corresponding intensity measure. The properties of this measure on loops lead us…
The use of degree-degree correlations to model realistic networks which are characterized by their Pearson's coefficient, has become widespread. However the effect on how different correlation algorithms produce different results on…
Interacting particle systems can often be constructed from a graphical representation, by applying local maps at the times of associated Poisson processes. This leads to a natural coupling of systems started in different initial states. We…
We propose a novel tree-based ensemble method, named XGBoostPP, to nonparametrically estimate the intensity of a point process as a function of covariates. It extends the use of gradient-boosted regression trees (Chen & Guestrin, 2016) to…
Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…
We present a novel Bayesian framework for inverse problems in which the pos terior distribution is interpreted as the intensity measure of a Poisson point process (PPP). The posterior density is approximated using kernel density estimation,…
The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant…
In this paper, we study invariant Poisson processes of lines (i.e, bi-infinite geodesics) in the $3$-regular tree. More precisely, there exists a unique (up to multiplicative constant) locally finite Borel measure on the space of lines that…
We present the Additive Poisson Process (APP), a novel framework that can model the higher-order interaction effects of the intensity functions in stochastic processes using lower dimensional projections. Our model combines the techniques…
Let $X$ be either $Z^d$ or the points of a Poisson process in $R^d$ of intensity 1. Given parameters $r$ and $p$, join each pair of points of $X$ within distance $r$ independently with probability $p$. This is the simplest case of a…
We consider a class of observation-driven Poisson count processes where the current value of the accompanying intensity process depends on previous values of both processes. We show under a contractive condition that the bivariate process…
We describe a set of new estimators for the N-point correlation functions of point processes. The variance of these estimators is calculated for the Poisson and binomial cases. It is shown that the variance of the unbiased estimator…
We consider near-critical two-dimensional statistical systems with boundary conditions inducing phase separation on the strip. By exploiting low-energy properties of two-dimensional field theories, we compute arbitrary $n$-point correlation…
The paper deals with disorders detection in the multivariate stochastic process. We consider the multidimensional Poisson process or the multivariate renewal process. This class of processes can be used as a description of the distributed…
Analytical approaches to model the structure of complex networks can be distinguished into two groups according to whether they consider an intensive (e.g., fixed degree sequence and random otherwise) or an extensive (e.g., adjacency…
The contact process is a simple model for the spread of an infection in a structured population. We investigate the case when the underlying structure evolves dynamically as a degree-dependent dynamical percolation model. Starting with a…
Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…
In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…
Statistical modeling of point patterns is an important and common problem in several areas. The Poisson process is the most common process used for this purpose, in particular, its generalization that considers the intensity function to be…
We consider the interlacement Poisson point process on the space of doubly-infinite Z^d-valued trajectories modulo time-shift, tending to infinity at positive and negative infinite times. The set of vertices and edges visited by at least…