Monte Carlo goodness-of-fit tests for degree corrected and related stochastic blockmodels
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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
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2016
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| _version_ | 1866911789626687488 |
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| author | Karwa, Vishesh Pati, Debdeep Petrović, Sonja Solus, Liam Alexeev, Nikita Raič, Mateja Wilburne, Dane Williams, Robert Yan, Bowei |
| author_facet | Karwa, Vishesh Pati, Debdeep Petrović, Sonja Solus, Liam Alexeev, Nikita Raič, Mateja Wilburne, Dane Williams, Robert Yan, Bowei |
| contents | 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 \emph{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 behavior.
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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1612_06040 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Monte Carlo goodness-of-fit tests for degree corrected and related stochastic blockmodels Karwa, Vishesh Pati, Debdeep Petrović, Sonja Solus, Liam Alexeev, Nikita Raič, Mateja Wilburne, Dane Williams, Robert Yan, Bowei Methodology Statistics Theory 62R01, 05C82 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 \emph{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 behavior. 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. |
| title | Monte Carlo goodness-of-fit tests for degree corrected and related stochastic blockmodels |
| topic | Methodology Statistics Theory 62R01, 05C82 |
| url | https://arxiv.org/abs/1612.06040 |