Estimating Parameters of a Probabilistic Heterogeneous Block Model via the EM Algorithm
We introduce a semiparametric block model for graphs, where the within- and between-cluster edge probabilities are not constants within the blocks but are described by logistic type models, reminiscent of the 50-year-old Rasch model and the newly introduced α-β models. Our purpose is to give a parti...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2015/657965 |
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| _version_ | 1849412967512145920 |
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| author | Marianna Bolla Ahmed Elbanna |
| author_facet | Marianna Bolla Ahmed Elbanna |
| author_sort | Marianna Bolla |
| collection | DOAJ |
| description | We introduce a semiparametric block model for graphs, where the within- and between-cluster edge probabilities are not constants within the blocks but are described by logistic type models, reminiscent of the 50-year-old Rasch model and the newly introduced α-β models. Our purpose is to give a partition of the vertices of an observed graph so that the induced subgraphs and bipartite graphs obey these models, where their strongly interlaced parameters give multiscale evaluation of the vertices at the same time. In this way, a profoundly heterogeneous version of the stochastic block model is built via mixtures of the above submodels, while the parameters are estimated with a special EM iteration. |
| format | Article |
| id | doaj-art-66506a41a8d54c42bb96841f5a74ee30 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-66506a41a8d54c42bb96841f5a74ee302025-08-20T03:34:17ZengWileyJournal of Probability and Statistics1687-952X1687-95382015-01-01201510.1155/2015/657965657965Estimating Parameters of a Probabilistic Heterogeneous Block Model via the EM AlgorithmMarianna Bolla0Ahmed Elbanna1Institute of Mathematics, Budapest University of Technology and Economics, Műegyetem Rakpart 3, Budapest 1111, HungaryInstitute of Mathematics, Budapest University of Technology and Economics, Műegyetem Rakpart 3, Budapest 1111, HungaryWe introduce a semiparametric block model for graphs, where the within- and between-cluster edge probabilities are not constants within the blocks but are described by logistic type models, reminiscent of the 50-year-old Rasch model and the newly introduced α-β models. Our purpose is to give a partition of the vertices of an observed graph so that the induced subgraphs and bipartite graphs obey these models, where their strongly interlaced parameters give multiscale evaluation of the vertices at the same time. In this way, a profoundly heterogeneous version of the stochastic block model is built via mixtures of the above submodels, while the parameters are estimated with a special EM iteration.http://dx.doi.org/10.1155/2015/657965 |
| spellingShingle | Marianna Bolla Ahmed Elbanna Estimating Parameters of a Probabilistic Heterogeneous Block Model via the EM Algorithm Journal of Probability and Statistics |
| title | Estimating Parameters of a Probabilistic Heterogeneous Block Model via the EM Algorithm |
| title_full | Estimating Parameters of a Probabilistic Heterogeneous Block Model via the EM Algorithm |
| title_fullStr | Estimating Parameters of a Probabilistic Heterogeneous Block Model via the EM Algorithm |
| title_full_unstemmed | Estimating Parameters of a Probabilistic Heterogeneous Block Model via the EM Algorithm |
| title_short | Estimating Parameters of a Probabilistic Heterogeneous Block Model via the EM Algorithm |
| title_sort | estimating parameters of a probabilistic heterogeneous block model via the em algorithm |
| url | http://dx.doi.org/10.1155/2015/657965 |
| work_keys_str_mv | AT mariannabolla estimatingparametersofaprobabilisticheterogeneousblockmodelviatheemalgorithm AT ahmedelbanna estimatingparametersofaprobabilisticheterogeneousblockmodelviatheemalgorithm |