Related papers: A cluster expansion approach to exponential random…
A well-known cluster expansion, which leads to virial expansion for the free energy of low density systems, is modified in such a way that it becomes applicable to the description of condensed state of matter. To this end, the averaging of…
A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…
Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple…
Exponential random graph models have attracted significant research attention over the past decades. These models are maximum-entropy ensembles under the constraints that the expected values of a set of graph observables are equal to given…
Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a…
Linked cluster expansions provide a useful tool both for analytical and numerical investigations of lattice field theories. The expansion parameter is the interaction strength fields at neighboured lattice sites are coupled. They result…
Although the community structure organization is one of the most important characteristics of real-world networks, the traditional network models fail to reproduce the feature. Therefore, the models are useless as benchmark graphs for…
Families of mixtures of multivariate power exponential (MPE) distributions have been previously introduced and shown to be competitive for cluster analysis in comparison to other elliptical mixtures including mixtures of Gaussian…
Ensembles of networks arise in many scientific fields, but there are few statistical tools for inferring their generative processes, particularly in the presence of both dyadic dependence and cross-graph heterogeneity. To fill in this gap,…
Random graphs with power-law degrees can model scale-free networks as sparse topologies with strong degree heterogeneity. Mathematical analysis of such random graphs proved successful in explaining scale-free network properties such as…
Nowadays, exponential random graphs (ERGs) are among the most widely-studied network models. Different analytical and numerical techniques for ERG have been developed that resulted in the well-established theory with true predictive power.…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
In [7], a cluster expansion method has been developed to study the fluctuations of the hard sphere dynamics around the Boltzmann equation. This method provides a precise control on the exponential moments of the empirical measure, from…
We consider a family of directed exponential random graph models parametrized by edges and outward stars. Much of the important statistical content of such models is given by the normalization constant of the models, and in particular, an…
Motivated by modern applications in which one constructs graphical models based on a very large number of features, this paper introduces a new class of cluster-based graphical models, in which variable clustering is applied as an initial…
Exponential-family random graph models (ERGMs) provide a principled and flexible way to model and simulate features common in social networks, such as propensities for homophily, mutuality, and friend-of-a-friend triad closure, through…
Limits of densities belonging to an exponential family appear in many applications, {e.g.} Gibbs models in Statistical Physics, relaxed combinatorial optimization, coding theory, critical likelihood computations, Bayes priors with singular…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
There has been an explosion of interest in statistical models for analyzing network data, and considerable interest in the class of exponential random graph (ERG) models, especially in connection with difficulties in computing maximum…
To understand how hidden information can be extracted from statistical networks, planted models in random graphs have been the focus of intensive study in recent years. In this work, we consider the detection of a planted matching, i.e., an…