Block models for multipartite networks.Applications in ecology and ethnobiology

Bar-Hen, Avner; Barbillon, Pierre; Donnet, Sophie

doi:10.48550/arxiv.1807.10138

Cited by 3 publications

(2 citation statements)

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“…• Planted Multipartite Hypergraph Model: Let n = rk and 0 < p < q < 1. This generalizes the multipartite graph models (e.g., [1,4]) to hypergraph models.…”

Section: Remark 3 Our Settings Cover the Following Classical Models W...mentioning

confidence: 80%

Information Theoretic Limits of Exact Recovery in Sub-hypergraph Models for Community Detection

Liang¹,

Ke²,

Honorio³

2021

Preprint

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In this paper, we study the information theoretic bounds for exact recovery in sub-hypergraph models for community detection. We define a general model called the m−uniform sub-hypergraph stochastic block model (m−ShSBM). Under the m−ShSBM, we use Fano's inequality to identify the region of model parameters where any algorithm fails to exactly recover the planted communities with a large probability. We also identify the region where a Maximum Likelihood Estimation (MLE) algorithm succeeds to exactly recover the communities with high probability. Our bounds are tight and pertain to the community detection problems in various models such as the planted hypergraph stochastic block model, the planted densest sub-hypergraph model, and the planted multipartite hypergraph model.

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“…• Planted Multipartite Hypergraph Model: Let n = rk and 0 < p < q < 1. This generalizes the multipartite graph models (e.g., [1,4]) to hypergraph models.…”

Section: Remark 3 Our Settings Cover the Following Classical Models W...mentioning

confidence: 80%

Information Theoretic Limits of Exact Recovery in Sub-hypergraph Models for Community Detection

Liang¹,

Ke²,

Honorio³

2021

Preprint

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“…If we release the constraint of the unique affiliation, then the inter-level can be modelled by a latent block model and we obtain a particular case of the multipartite SBM of Bar-Hen et al (2018). However, then the interactions between individuals and organisations are considered on the same level as the affiliations, and the clustering might be strongly influenced by the number of individuals in each organisation.…”

Section: Introductionmentioning

confidence: 99%

A Stochastic Block Model Approach for the Analysis of Multilevel Networks: an Application to the Sociology of Organizations

Chabert-Liddell,

Barbillon,

Donnet

et al. 2019

Preprint

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This work is motivated by the analysis of multilevel networks. We define a multilevel network as the junction of two interaction networks, one level representing the interactions between individuals and the other one the interactions between organisations. The levels are linked by an affiliation relationship, each individual belonging to a unique organisation. We design a Stochastic block model (SBM) suited to multilevel networks. SBM is a latent variable model for networks, where the connections between nodes depend on a latent clustering (blocks), thus modeling some connection heterogeneity. We prove the identifiability of our model. The parameters of the model are estimated with a variational EM algorithm. An Integrated Completed Likelihood criterion is developed not only to select the number of blocks but also to detect whether the two levels (individuals and organisations) are dependent or not. In a comprehensive simulation study, we exhibit the benefit of considering our approach, illustrate the robustness of our parameter estimation and highlight the reliability of our model selection criterion. Our approach is applied on a sociological dataset collected during a television programmers trade fare. The inter-organisational level is the economic networks between companies and the inter-individual level is the informal network between their representatives.

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