An Exponential Family of Probability Distributions for Directed Graphs

By Paul Holland, S. Leinhardt. 1981

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Citations in the corpus

NetGAN: Generating Graphs via Random Walks (2018, background): “ERGM seems to be performing surprisingly well, however it suffers from severe overfitting – using the same fitted ERGM for the link prediction task we get both AUC and AP scores close to 0.5 (worst possible value).”
Asymmetric Transitivity Preserving Graph Embedding (2016, background): “[12] propose the p 1 distribution model to capture the structural properties in directed graph, including the atrrac-tiveness and expansiveness of vertexes and the reciprocation of edges.”
Designing Random Graph Models Using Variational Autoencoders With Applications to Chemical Design (2018, methodology): “L G ] 1 4 Fe block models [21], Kronecker graph models [28] or exponential random graphs (ERGM) [18], which make strong (parametric) assumptions about the underlying generative process of the graphs they model and, as a consequence, have a limited expressive power.”
The Structure and Function of Complex Networks (2003, methodology): “In this and the following section we describe two candidate models, the Markov graphs of Holland and Leinhardt [194] and Strauss [160, 385] and the small-world model of Watts and Strogatz [416].”
The analysis of social networks (2008, background): “Holland and Leinhardt (1981) introduced the p1 probability density including the homogeneity conditions lij = l and qij = q for all i and j, and treating the sets of parameters {ai} and {cj} as fixed effects.”
Statistical Models for Social Networks (2011, background): “A review of network formation models in economics is given by Jackson (2005), and the extensive work in this area has led to three recent books: Goyal (2007), Vega-Redondo (2007), and Jackson (2008).”
NeVAE: A Deep Generative Model for Molecular Graphs (2018, background): “i et al. [31], which just got accepted at ICLR 2018 at the time of writing. 1 arXiv:1802.05283v1 [cs.LG] 14 Feb 2018 block models [21], Kronecker graph models [28] or exponential random graphs (ERGM) [18], which make strong (parametric) assumptions about the underlying generative process of the grap”
Networks beyond pairwise interactions: structure and dynamics (2020, methodology): “IV A 1, Markov random graphs [163, 164] and their exponential random graph model (ERGM) generalization [161] have been proposed early on to fulfill this role.”
Econometrics of Network Formation (2016, background): “The solution to this problem lies in a literature in statistics going back to Holland and Leinhardt (1981).”
p2: a random effects model with covariates for directed graphs (2004, methodology): “Identification restrictions are needed for a and b, e.g., a1 ¼ b1 ¼ 0 or P iai ¼ P jbj¼0 as in HOLLAND and LEINHARDT (1981).”
Goodness of Fit of Social Network Models (2008, unknown): “Much recent effort has been focused on inference for social network models (e.g., Holland and Leinhardt 1981; Strauss and Ikeda 1990; Snijders 2002; Hunter and Handcock 2006), but comparatively little work has tested the goodness of ﬁt of the models.”
Networks and the Epidemiology of Infectious Disease (2010, methodology): “ERGMs were first introduced in the early 1980s by Holland and Leinhardt [79] based on the work of Besag [80].”
Statistical mechanics of networks. (2004, methodology): “Exponential random graphs were first proposed in the early 1980s by Holland and Leinhardt [9], building on statistical foundations laid by Besag [10].”