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We define a general class of network formation models, Statistical Exponential Random Graph Models (SERGMs), that nest standard exponential random graph models (ERGMs) as a special case. We provide the first general results on when these…
Exponential random graph models, or ERGMs, are a flexible and general class of models for modeling dependent data. While the early literature has shown them to be powerful in capturing many network features of interest, recent work…
This note explores the applicability of unsupervised machine learning techniques towards hard optimization problems on random inputs. In particular we consider Graph Neural Networks (GNNs) -- a class of neural networks designed to learn…
In this paper, we study the application of quasi-Newton methods for solving empirical risk minimization (ERM) problems defined over a large dataset. Traditional deterministic and stochastic quasi-Newton methods can be executed to solve such…
We extend the well-known and widely used Exponential Random Graph Model (ERGM) by including nodal random effects to compensate for heterogeneity in the nodes of a network. The Bayesian framework for ERGMs proposed by Caimo and Friel (2011)…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
The exponential family random graph modeling (ERGM) framework provides a flexible approach for the statistical analysis of networks. As ERGMs typically involve normalizing factors that are costly to compute, practical inference relies on a…
Random graphs, where the connections between nodes are considered random variables, have wide applicability in the social sciences. Exponential-family Random Graph Models (ERGM) have shown themselves to be a useful class of models for…
The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the…
With the growth of interest in network data across fields, the Exponential Random Graph Model (ERGM) has emerged as the leading approach to the statistical analysis of network data. ERGM parameter estimation requires the approximation of an…
Social networks as a representation of relational data, often possess multiple types of dependency structures at the same time. There could be clustering (beyond homophily) at a macro level as well as transitivity (a friend's friend is more…
Many popular models from the networks literature can be viewed through a common lens of contingency tables on network dyads, resulting in \emph{log-linear ERGMs}: exponential family models for random graphs whose sufficient statistics are…
Group-based brain connectivity networks have great appeal for researchers interested in gaining further insight into complex brain function and how it changes across different mental states and disease conditions. Accurately constructing…
Exponential random graph models (ERGMs) are flexible probabilistic frameworks to model statistical networks through a variety of network summary statistics. Conventional Bayesian estimation for ERGMs involves iteratively exchanging with an…
Ensembles of networks arise in various fields where multiple independent networks are observed on the same set of nodes, for example, a collection of brain networks constructed on the same brain regions for different individuals. However,…
Traditional network analysis focuses on binary edges, while real-world relationships are more nuanced, encompassing cooperation, neutrality, and conflict. The rise of negative edges in social media discussions spurred interest in analyzing…
Temporal exponential random graph models (TERGM) are powerful statistical models that can be used to infer the temporal pattern of edge formation and elimination in complex networks (e.g., social networks). TERGMs can also be used in a…
Analysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks, related to their biological functions.…
Exponential-family random graph models (ERGMs) provide a principled way to model and simulate features common in human social networks, such as propensities for homophily and friend-of-a-friend triad closure. We show that, without…
The exponential-family random graph models (ERGMs) have emerged as an important framework for modeling social networks for a wide variety of relational types. ERGMs for valued networks are less well-developed than their unvalued…