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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.00188 |
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| _version_ | 1866913218696314880 |
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| author | Gunderson, Lee M Bravo-Hermsdorff, Gecia Orbanz, Peter |
| author_facet | Gunderson, Lee M Bravo-Hermsdorff, Gecia Orbanz, Peter |
| contents | In this work, we describe a method that determines an exact map from a finite set of subgraph densities to the parameters of a stochastic block model (SBM) matching these densities. Given a number $K$ of blocks, the subgraph densities of a finite number of stars and bistars uniquely determines a single element of the class of all degree-separated stochastic block models with $K$ blocks. Our method makes it possible to translate estimates of these subgraph densities into model parameters, and hence to use subgraph densities directly for inference. The computational overhead is negligible; computing the translation map is polynomial in $K$, but independent of the graph size once the subgraph densities are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00188 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Graph Pencil Method: Mapping Subgraph Densities to Stochastic Block Models Gunderson, Lee M Bravo-Hermsdorff, Gecia Orbanz, Peter Discrete Mathematics Combinatorics Statistics Theory In this work, we describe a method that determines an exact map from a finite set of subgraph densities to the parameters of a stochastic block model (SBM) matching these densities. Given a number $K$ of blocks, the subgraph densities of a finite number of stars and bistars uniquely determines a single element of the class of all degree-separated stochastic block models with $K$ blocks. Our method makes it possible to translate estimates of these subgraph densities into model parameters, and hence to use subgraph densities directly for inference. The computational overhead is negligible; computing the translation map is polynomial in $K$, but independent of the graph size once the subgraph densities are given. |
| title | The Graph Pencil Method: Mapping Subgraph Densities to Stochastic Block Models |
| topic | Discrete Mathematics Combinatorics Statistics Theory |
| url | https://arxiv.org/abs/2402.00188 |