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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2410.06223 |
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| _version_ | 1866917950733156352 |
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| author | Bortner, Cashous Garbett, Jennifer Gross, Elizabeth McClain, Christopher Krawzik, Naomi Young, Derek |
| author_facet | Bortner, Cashous Garbett, Jennifer Gross, Elizabeth McClain, Christopher Krawzik, Naomi Young, Derek |
| contents | Log-linear exponential random graph models are a specific class of statistical network models that have a log-linear representation. This class includes many stochastic blockmodel variants. In this paper, we focus on $β$-stochastic blockmodels, which combine the $β$-model with a stochastic blockmodel. Here, using recent results by Almendra-Hernández, De Loera, and Petrović, which describe a Markov basis for $β$-stochastic block model, we give a closed form formula for the maximum likelihood degree of a $β$-stochastic blockmodel. The maximum likelihood degree is the number of complex solutions to the likelihood equations. In the case of the $β$-stochastic blockmodel, the maximum likelihood degree factors into a product of Eulerian numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06223 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximum likelihood degree of the $β$-stochastic blockmodel Bortner, Cashous Garbett, Jennifer Gross, Elizabeth McClain, Christopher Krawzik, Naomi Young, Derek Statistics Theory Log-linear exponential random graph models are a specific class of statistical network models that have a log-linear representation. This class includes many stochastic blockmodel variants. In this paper, we focus on $β$-stochastic blockmodels, which combine the $β$-model with a stochastic blockmodel. Here, using recent results by Almendra-Hernández, De Loera, and Petrović, which describe a Markov basis for $β$-stochastic block model, we give a closed form formula for the maximum likelihood degree of a $β$-stochastic blockmodel. The maximum likelihood degree is the number of complex solutions to the likelihood equations. In the case of the $β$-stochastic blockmodel, the maximum likelihood degree factors into a product of Eulerian numbers. |
| title | Maximum likelihood degree of the $β$-stochastic blockmodel |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2410.06223 |