# Exponential-Family Models of Random Graphs: Inference in Finite, Super and Infinite Population Scenarios

@article{Schweinberger2017ExponentialFamilyMO, title={Exponential-Family Models of Random Graphs: Inference in Finite, Super and Infinite Population Scenarios}, author={M. Schweinberger and Pavel N. Krivitsky and C. Butts and J. Stewart}, journal={arXiv: Methodology}, year={2017} }

Exponential-family Random Graph Models (ERGMs) constitute a large statistical framework for modeling sparse and dense random graphs, short- and long-tailed degree distributions, covariates, and a wide range of complex dependencies. Special cases of ERGMs are generalized linear models (GLMs), Bernoulli random graphs, $\beta$-models, $p_1$-models, and models related to Markov random fields in spatial statistics and other areas of statistics. While widely used in practice, questions have been… Expand

#### 26 Citations

Consistent structure estimation of exponential-family random graph models with block structure

- Mathematics
- 2017

We consider the challenging problem of statistical inference for exponential-family random graph models based on a single observation of a random graph with complex dependence. To facilitate… Expand

Finite Mixtures of ERGMs for Modeling Ensembles of Networks

- Computer Science
- 2019

This work develops a Metropolis-within-Gibbs algorithm to conduct fully Bayesian inference and adapt a version of deviance information criterion for missing data models to choose the number of latent heterogeneous generative mechanisms. Expand

Exponential random graph model parameter estimation for very large directed networks

- Computer Science, Mathematics
- PloS one
- 2020

An implementation of the recently published Equilibrium Expectation (EE) algorithm for ERGM parameter estimation of large directed networks, and its application to an online social network with over 1.6 million nodes is demonstrated. Expand

Selection of Exponential-Family Random Graph Models via Held-Out Predictive Evaluation (HOPE)

- Mathematics, Computer Science
- 2019

This work proposes a predictive evaluation strategy for exponential family random graph models that is analogous to cross-validation and builds on the held-out predictive evaluation scheme, which can assist researchers in improving models by indicating where a model performs poorly, and by quantitatively comparing predictive performance across competing models. Expand

Exponential-Family Random Graph Models for Multi-Layer Networks.

- Medicine, Computer Science
- Psychometrika
- 2020

Extensions to ERGMs are introduced to address limitations: Conway-Maxwell-Binomial distribution to model the marginal dependence among multiple layers; a "layer logic" language to translate familiar ERGM effects to substantively meaningful interactions of observed layers; and nondegenerate triadic and degree effects. Expand

Impact of survey design on estimation of exponential-family random graph models from egocentrically-sampled data

- Computer Science
- 2021

This paper discusses how design choices for egocentric network studies impact statistical estimation and inference for ERGMs, and discusses the importance of harmonising measurement specifications across egos and alters. Expand

Analysis of Networks via the Sparse β-Model

- Computer Science
- 2019

This work proposes the Sparse β-Model, a new network model that interpolates the celebrated Erd˝os-R´enyi model and the β-model that assigns one diﬀerent parameter to each node, and shows via a monotonicity lemma that the seemingly combinatorial computational problem due to the `0-penalty can be overcome by assigning nonzero parameters to those nodes with the largest degrees. Expand

Score-Driven Exponential Random Graphs: A New Class of Time-Varying Parameter Models for Dynamical Networks

- Mathematics, Economics
- 2019

This work demonstrates the flexibility of the score-driven ERGMs, both as data generating processes and as filters, and proves the advantages of the dynamic version with respect to the static one, and allows for a test discriminating between static or time-varying parameters. Expand

Additive and Multiplicative Effects Network Models

- Mathematics
- 2018

Network datasets typically exhibit certain types of statistical dependencies, such as within-dyad correlation, row and column heterogeneity, and third-order dependence patterns such as transitivity… Expand

On Estimation and Inference in Latent Structure Random Graphs

- Mathematics
- 2018

We define a latent structure model (LSM) random graph as a random dot product graph (RDPG) in which the latent position distribution incorporates both probabilistic and geometric constraints,… Expand

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