Related papers: Maximizing graph probability under conditionally e…
Random graph models are frequently used as a controllable and versatile data source for experimental campaigns in various research fields. Generating such data-sets at scale is a non-trivial task as it requires design decisions typically…
It is often desirable to assess how well a given dataset is described by a given model. In network science, for instance, one often wants to say that a given real-world network appears to come from a particular network model. In statistical…
The maximum likelihood threshold (MLT) of a graph $G$ is the minimum number of samples to almost surely guarantee existence of the maximum likelihood estimate in the corresponding Gaussian graphical model. Recently a new characterization of…
Graphical Gaussian models have proven to be useful tools for exploring network structures based on multivariate data. Applications to studies of gene expression have generated substantial interest in these models, and resulting recent…
The abundance of models of complex networks and the current insufficient validation standards make it difficult to judge which models are strongly supported by data and which are not. We focus here on likelihood maximization methods for…
Random graph models have played a dominant role in the theoretical study of networked systems. The Poisson random graph of Erdos and Renyi, in particular, as well as the so-called configuration model, have served as the starting point for…
Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be…
Exchangeable random graphs serve as an important probabilistic framework for the statistical analysis of network data. In this work we develop an alternative parameterization for a large class of exchangeable random graphs, where the nodes…
We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their…
We consider the problem of sending a message from a sender $s$ to a receiver $r$ through an unreliable network by specifying in a protocol what each vertex is supposed to do if it receives the message from one of its neighbors. A protocol…
Components of complex systems are often classified according to the way they interact with each other. In graph theory such groups are known as clusters or communities. Many different techniques have been recently proposed to detect them,…
Inference of the network structure (e.g., routing topology) and dynamics (e.g., link performance) is an essential component in many network design and management tasks. In this paper we propose a new, general framework for analyzing and…
This article investigates and compares three approaches to link prediction in colaboration networks, namely, an ERGM (Exponential Random Graph Model; Robins et al. 2007), a GCN (Graph Convolutional Network; Kipf and Welling 2017), and a…
Probabilistic graphical models (PGMs) are widely used to discover latent structure in data, but their success hinges on selecting an appropriate model design. In practice, model specification is difficult and often requires iterative…
In this article the problem of reconstructing the pattern of connection between agents from partial empirical data in a macro-economic model is addressed, given a set of behavioral equations. This systemic point of view puts the focus on…
Because of the huge number of graphs possible even with a small number of nodes, inference on network structure is known to be a challenging problem. Generating large random directed graphs with prescribed probabilities of occurrences of…
Many network datasets exhibit connectivity with variance by resolution and large-scale organization that coexists with localized departures. When vertices have observed ordering or embedding, such as geography in spatial and village…
Estimating the matrix of connections probabilities is one of the key questions when studying sparse networks. In this work, we consider networks generated under the sparse graphon model and the in-homogeneous random graph model with missing…
We develop a maximum-likelihood based method for regression in a setting where the dependent variable is a random graph and covariates are available on a graph-level. The model generalizes the well-known $\beta$-model for random graphs by…
The Expectation--Maximization (EM) algorithm is a simple meta-algorithm that has been used for many years as a methodology for statistical inference when there are missing measurements in the observed data or when the data is composed of…