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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.14464 |
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| _version_ | 1866910277922979840 |
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| author | Majumdar, Sourav |
| author_facet | Majumdar, Sourav |
| contents | We propose exact conditional goodness-of-fit tests for directed mixed membership stochastic block models. Given dyad-level sender and receiver roles, the block-pair edge totals are sufficient for the block probability matrix; conditioning on these totals gives a nuisance-free uniform law on a finite fiber. This yields finite-sample randomization tests for residual sender and receiver heterogeneity, reciprocity, and directed transitive closure. The procedure uses an independent fiber sampler, Monte Carlo rank \(p\)-values, and can be applied after drawing latent block-pair assignments from the posterior distribution. Simulations and the Sampson monastery network show that the tests are calibrated under the null and diagnostically useful for directed model misspecification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14464 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact conditional goodness-of-fit tests for the mixed membership stochastic block model Majumdar, Sourav Methodology We propose exact conditional goodness-of-fit tests for directed mixed membership stochastic block models. Given dyad-level sender and receiver roles, the block-pair edge totals are sufficient for the block probability matrix; conditioning on these totals gives a nuisance-free uniform law on a finite fiber. This yields finite-sample randomization tests for residual sender and receiver heterogeneity, reciprocity, and directed transitive closure. The procedure uses an independent fiber sampler, Monte Carlo rank \(p\)-values, and can be applied after drawing latent block-pair assignments from the posterior distribution. Simulations and the Sampson monastery network show that the tests are calibrated under the null and diagnostically useful for directed model misspecification. |
| title | Exact conditional goodness-of-fit tests for the mixed membership stochastic block model |
| topic | Methodology |
| url | https://arxiv.org/abs/2507.14464 |