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

Schweinberger, Michael

doi:10.3150/19-bej1153

Cited by 9 publications

(5 citation statements)

References 73 publications

(199 reference statements)

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“…In terms of computational complexity, a crucial avenue would involve determining the theoretical distribution for dissimilarity, ultimately contributing to significant reductions in computational overhead. Furthermore, the proposed framework can be extended to incorporate more sophisticated block models, such as exponential [44], multilevel [45], and dynamic [46] models, offering additional benefits and insights.…”

Section: Discussionmentioning

confidence: 99%

Dissimilarity-based hypothesis testing for community detection in heterogeneous networks

Xu,

Chen,

Mendes

2023

Front. Phys.

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Identifying communities within networks is a crucial and challenging problem with practical implications across various scientific fields. Existing methods often overlook the heterogeneous distribution of nodal degrees or require prior knowledge of the number of communities. To overcome these limitations, we propose an efficient hypothesis test for community detection by quantifying dissimilarities between graphs. Our approach centers around examining the dissimilarity between a given random graph and a null hypothesis which assumes a degree-corrected Erdös–Rényi type. To compare the dissimilarity, we introduce a measure that takes into account the distributions of vertex distances, clustering coefficients, and alpha-centrality. This measure is then utilized in our hypothesis test. To simultaneously uncover the number of communities and their corresponding structures, we develop a two-stage bipartitioning algorithm. This algorithm integrates seamlessly with our hypothesis test and enables the exploration of community organization within the network. Through experiments conducted on both synthetic and real networks, we demonstrate that our method outperforms state-of-the-art approaches in community detection.

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Section: Discussionmentioning

confidence: 99%

Dissimilarity-based hypothesis testing for community detection in heterogeneous networks

Xu,

Chen,

Mendes

2023

Front. Phys.

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“…For instance, Box-Steffensmeier et al (2018) discuss how unmeasured nodal covariates can contribute to omitted variable bias and model degeneracy. Schweinberger and colleagues (Schweinberger 2020;Schweinberger and Handcock 2015;Stewart et al 2019) develop a similar argument for the broader case of nesting structure, where accounting for nesting structure improves estimation of decay parameters and out-of-sample statistics for triad and degree distributions in curved ERGMs (see Stewart et al 2019). Kim et al (2016) document that measurement error during network data collection can generate inaccurate sufficient statistics that bias ERGM coefficients.…”

Section: Sources Of Scalingmentioning

confidence: 92%

“…While recent studies have sought to address several sources of residual variation, including unobserved heterogeneity (unmeasured nodal covariates; Box-Steffensmeier, Christenson, and Morgan 2018; Thiemichen et al 2016; van Duijn, Snijders, and Zijlstra 2004), nesting structure (Schweinberger 2020; Schweinberger and Handcock 2015; Stewart et al 2019), and measurement error (Kim, Leonardo, and Kirkland 2016), the consequences of scaling for statistical inference using ERGM have been largely overlooked. In addition to these sources, we show that scaling can affect ERGM results even when omitted variables are uncorrelated with other predictors .…”

mentioning

confidence: 99%

The Problem of Scaling in Exponential Random Graph Models

Duxbury

2021

Sociological Methods & Research

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This study shows that residual variation can cause problems related to scaling in exponential random graph models (ERGM). Residual variation is likely to exist when there are unmeasured variables in a model—even those uncorrelated with other predictors—or when the logistic form of the model is inappropriate. As a consequence, coefficients cannot be interpreted as effect sizes or compared between models and homophily coefficients, as well as other interaction coefficients, cannot be interpreted as substantive effects in most ERGM applications. We conduct a series of simulations considering the substantive impact of these issues, revealing that realistic levels of residual variation can have large consequences for ERGM inference. A flexible methodological framework is introduced to overcome these problems. Formal tests of mediation and moderation are also proposed. These methods are applied to revisit the relationship between selective mixing and triadic closure in a large AddHealth school friendship network. Extensions to other classes of statistical work models are discussed.

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“… 2013 ; Gross et al. 2021 ; Schweinberger 2020 ; Schweinberger and Handcock 2015 ; Schweinberger and Luna 2018 ; Wang et al. 2019 ), samples from larger networks (An 2016 ; Handcock and Gile 2010 ; Pattison et al.…”

Section: Exponential Random Graph Modelsmentioning

confidence: 99%

Testing biological network motif significance with exponential random graph models

Stivala

Lomi

2021

Appl Netw Sci

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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. However, there is disagreement as to the statistical significance of these motifs, and there are potential problems with standard methods for estimating this significance. Exponential random graph models (ERGMs) are a class of statistical model that can overcome some of the shortcomings of commonly used methods for testing the statistical significance of motifs. ERGMs were first introduced into the bioinformatics literature over 10 years ago but have had limited application to biological networks, possibly due to the practical difficulty of estimating model parameters. Advances in estimation algorithms now afford analysis of much larger networks in practical time. We illustrate the application of ERGM to both an undirected protein–protein interaction (PPI) network and directed gene regulatory networks. ERGM models indicate over-representation of triangles in the PPI network, and confirm results from previous research as to over-representation of transitive triangles (feed-forward loop) in an E. coli and a yeast regulatory network. We also confirm, using ERGMs, previous research showing that under-representation of the cyclic triangle (feedback loop) can be explained as a consequence of other topological features.

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

Cited by 9 publications

References 73 publications

Dissimilarity-based hypothesis testing for community detection in heterogeneous networks

Dissimilarity-based hypothesis testing for community detection in heterogeneous networks

The Problem of Scaling in Exponential Random Graph Models

Testing biological network motif significance with exponential random graph models

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