Hybrid of node and link communities for graphon estimation
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911753874440192 |
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| author | Verdeyme, Arthur Olhede, Sofia C. |
| author_facet | Verdeyme, Arthur Olhede, Sofia C. |
| contents | Networks serve as a tool used to examine the large-scale connectivity patterns in complex systems. Modelling their generative mechanism nonparametrically is often based on step-functions, such as the stochastic block models. These models are capable of addressing two prominent topics in network science: link prediction and community detection. However, such methods often have a resolution limit, making it difficult to separate small-scale structures from noise. To arrive at a smoother representation of the network's generative mechanism, we explicitly trade variance for bias by smoothing blocks of edges based on stochastic equivalence. As such, we propose a different estimation method using a new model, which we call the stochastic shape model. Typically, analysis methods are based on modelling node or link communities. In contrast, we take a hybrid approach, bridging the two notions of community. Consequently, we obtain a more parsimonious representation, enabling a more interpretable and multiscale summary of the network structure. By considering multiple resolutions, we trade bias and variance to ensure that our estimator is rate-optimal. We also examine the performance of our model through simulations and applications to real network data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05088 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hybrid of node and link communities for graphon estimation Verdeyme, Arthur Olhede, Sofia C. Methodology Probability Statistics Theory Networks serve as a tool used to examine the large-scale connectivity patterns in complex systems. Modelling their generative mechanism nonparametrically is often based on step-functions, such as the stochastic block models. These models are capable of addressing two prominent topics in network science: link prediction and community detection. However, such methods often have a resolution limit, making it difficult to separate small-scale structures from noise. To arrive at a smoother representation of the network's generative mechanism, we explicitly trade variance for bias by smoothing blocks of edges based on stochastic equivalence. As such, we propose a different estimation method using a new model, which we call the stochastic shape model. Typically, analysis methods are based on modelling node or link communities. In contrast, we take a hybrid approach, bridging the two notions of community. Consequently, we obtain a more parsimonious representation, enabling a more interpretable and multiscale summary of the network structure. By considering multiple resolutions, we trade bias and variance to ensure that our estimator is rate-optimal. We also examine the performance of our model through simulations and applications to real network data. |
| title | Hybrid of node and link communities for graphon estimation |
| topic | Methodology Probability Statistics Theory |
| url | https://arxiv.org/abs/2401.05088 |