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Abstract In this paper, we consider data consisting of multiple networks, each composed of a different edge set on a common set of nodes. Many models have been proposed for the analysis of suchmultiviewnetwork data under the assumption that the data views are closely related. In this paper, we provide tools for evaluating this assumption. In particular, we ask: given two networks that each follow a stochastic block model, is there an association between the latent community memberships of the nodes in the two networks? To answer this question, we extend the stochastic block model for a single network view to the two‐view setting, and develop a new hypothesis test for the null hypothesis that the latent community memberships in the two data views are independent. We apply our test to protein–protein interaction data from the HINT database. We find evidence of a weak association between the latent community memberships of proteins defined with respect to binary interaction data and the latent community memberships of proteins defined with respect to cocomplex association data. We also extend this proposal to the setting of a network with node covariates. The proposed methods extend readily to three or more network/multivariate data views.
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Monte Carlo goodness-of-fit tests for degree corrected and related stochastic blockmodels
Abstract We construct Bayesian and frequentist finite-sample goodness-of-fit tests for three different variants of the stochastic blockmodel for network data. Since all of the stochastic blockmodel variants are log-linear in form when block assignments are known, the tests for the latent block model versions combine a block membership estimator with the algebraic statistics machinery for testing goodness-of-fit in log-linear models. We describe Markov bases and marginal polytopes of the variants of the stochastic blockmodel and discuss how both facilitate the development of goodness-of-fit tests and understanding of model behaviour. The general testing methodology developed here extends to any finite mixture of log-linear models on discrete data, and as such is the first application of the algebraic statistics machinery for latent-variable models.
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- Award ID(s):
- 1947919
- PAR ID:
- 10463118
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Volume:
- 86
- Issue:
- 1
- ISSN:
- 1369-7412
- Format(s):
- Medium: X Size: p. 90-121
- Size(s):
- p. 90-121
- Sponsoring Org:
- National Science Foundation
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