Related papers: Local Graph Stability in Exponential Family Random…

We study properties of Graph Convolutional Networks (GCNs) by analyzing their behavior on standard models of random graphs, where nodes are represented by random latent variables and edges are drawn according to a similarity kernel. This…

Graph convolutional neural networks (GCNNs) have emerged as powerful tools for analyzing graph-structured data, achieving remarkable success across diverse applications. However, the theoretical understanding of the stability of these…

Population structure affects the outcome of natural selection. Static population structures can be described by graphs, where individuals occupy the nodes, and interactions occur along the edges. General conditions for evolutionary success…

Exponential random graph models (ERGMs) are flexible probability models allowing edge dependency. However, it is known that, to a first-order approximation, many ERGMs behave like Erd\"os-R\'enyi random graphs, where edges are independent.…

By comparing the evolution of the local and equal load sharing fiber bundle models, we point out the paradoxical result that stresses seem to make the local load sharing model stable when the equal load sharing model is not. We explain this…

Stable random variables are motivated by the central limit theorem for densities with (potentially) unbounded variance and can be thought of as natural generalizations of the Gaussian distribution to skewed and heavy-tailed phenomenon. In…

Conventionally, pairwise relationships between nodes are considered to be the fundamental building blocks of complex networks. However, over the last decade the overabundance of certain sub-network patterns, so called motifs, has attracted…

We consider the problem of estimating the parameters in a pairwise graphical model in which the distribution of each node, conditioned on the others, may have a different parametric form. In particular, we assume that each node's…

This article discusses the problem of determining whether a given point, or set of points, lies within the convex hull of another set of points in $d$ dimensions. This problem arises naturally in a statistical context when using a…

The exponential family of random graphs represents an important and challenging class of network models. Despite their flexibility, conventionally used exponential random graphs have one shortcoming. They cannot directly model weighted…

The stable matching problem is a prototype model in economics and social sciences where agents act selfishly to optimize their own satisfaction, subject to mutually conflicting constraints. A stable matching is a pairing of adjacent…

Graph neural networks are experiencing a surge of popularity within the machine learning community due to their ability to adapt to non-Euclidean domains and instil inductive biases. Despite this, their stability, i.e., their robustness to…

An important challenge in the field of exponential random graphs (ERGs) is the fitting of non-trivial ERGs on large graphs. By utilizing fast matrix block-approximation techniques, we propose an approximative framework to such non-trivial…

Temporal exponential-family random graph models (TERGMs) are a flexible class of network models for the dynamics of tie formation and dissolution. In practice, separable TERGMs (STERGMs) are the subclass most often used, as these permit…

Graph convolutional networks (GCNs) have emerged as powerful models for graph learning tasks, exhibiting promising performance in various domains. While their empirical success is evident, there is a growing need to understand their…

Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…

Graph neural networks (GNN) have shown great advantages in many graph-based learning tasks but often fail to predict accurately for a task-based on sets of nodes such as link/motif prediction and so on. Many works have recently proposed to…

In the problem of structured prediction with graph representation learning (GRL for short), the hypothesis returned by the algorithm maps the set of features in the \emph{receptive field} of the targeted vertex to its label. To understand…

Geometric variations like rotation, scaling, and viewpoint changes pose a significant challenge to visual understanding. One common solution is to directly model certain intrinsic structures, e.g., using landmarks. However, it then becomes…

In this paper, we study exponential random graph models subject to certain constraints. We obtain some general results about the asymptotic structure of the model. We show that there exists non-trivial regions in the phase plane where the…