[Paper Review] Block models for multipartite networks.Applications in ecology and ethnobiology

Avner Bar‐Hen, Pierre Barbillon+1 more|arXiv (Cornell University)|Jul 26, 2018

Bayesian Methods and Mixture Models34 references6 citations

TL;DR

This paper introduces the Multipartite Blocks Model (MBM), a generative probabilistic model that identifies clusters of nodes with similar connectivity patterns across multiple interrelated networks—such as ecological mutualistic systems or ethnobiological seed exchange networks. Using a variational Expectation-Maximization algorithm and an Integrated Completed Likelihood criterion for model selection, the MBM effectively uncovers latent block structures in generalized multipartite networks, as demonstrated on real ecological and ethnobiological datasets with reproducible results via the GREMLIN R package.

ABSTRACT

Modeling relations between individuals is a classical question in social sciences, ecology, etc. In order to uncover a latent structure in the data, a popular approach consists in clustering individuals according to the observed patterns of interactions. To do so, Stochastic block models (SBM) and Latent Block models (LBM) are standard tools for clustering the individuals with respect to their comportment in a unique network. However, when adopting an integrative point of view, individuals are not involved in a unique network but are part of several networks, resulting into a potentially complex multipartite network. In this contribution, we propose a stochastic block model able to handle multipartite networks, thus supplying a clustering of the individuals based on their connection behavior in more than one network. Our model is an extension of the latent block models (LBM) and stochastic block model (SBM). The parameters -- such as the marginal probabilities of assignment to blocks and the matrix of probabilities of connections between blocks -- are estimated through a variational Expectation-Maximization procedure. The numbers of blocks are chosen with the Integrated Completed Likelihood criterion, a penalized likelihood criterion. The pertinence of our methodology is illustrated on two datasets issued from ecology and ethnobiology.

Motivation & Objective

• To address the lack of statistical tools for jointly analyzing multiple interrelated networks involving common nodes.
• To model generalized multipartite networks where interactions occur both between and within functional groups.
• To identify latent clusters of nodes sharing similar connectivity patterns across multiple network layers.
• To develop a robust inference procedure for estimating block structures and selecting the optimal number of clusters.
• To demonstrate the model's utility on real-world ecological and ethnobiological datasets.

Proposed method

• Proposes a generative probabilistic model, the Multipartite Blocks Model (MBM), which assumes each functional group is partitioned into clusters with homogeneous connection behaviors.
• Uses latent variables to model edge probabilities as a mixture over block memberships, enabling joint analysis of multiple network types.
• Employs a variational Expectation-Maximization (VEM) algorithm to approximate the intractable likelihood and estimate model parameters.
• Applies an Integrated Completed Likelihood (ICL) criterion tailored for MBM to select the optimal number of clusters in each functional group.
• Incorporates conjugate priors (beta and gamma) for robust Bayesian estimation and uses asymptotic approximations for model scoring.
• Implements the inference pipeline in the GREMLIN R package, with simulations and case studies provided as reproducible vignettes.

Experimental results

Research questions

• RQ1 How can we jointly model multiple interrelated networks involving the same set of nodes, especially when interactions occur both between and within functional groups?
• RQ2 What is the optimal number of latent clusters in each functional group that best explains the observed connectivity patterns across multiple networks?
• RQ3 Can a probabilistic block model effectively uncover meaningful community structures in complex generalized multipartite networks from ecology and ethnobiology?
• RQ4 How does the proposed variational inference approach compare to other clustering methods in terms of robustness and accuracy on simulated and real data?
• RQ5 To what extent can the MBM reveal biologically or socially meaningful patterns in ecological mutualism and seed exchange networks?

Key findings

• The MBM successfully identifies distinct clusters of plants, pollinators, ants, and birds in a plant-animal interaction network, with estimated block probabilities revealing specific interaction patterns such as high connectivity between plant species 4 and 5 with birds and ants.
• In the seed circulation dataset, the model reveals that farmers in cluster 3 are highly connected to crop species in cluster 1, with estimated block probabilities showing strong seed exchange patterns between specific farmer and crop clusters.
• The ICL-based model selection procedure effectively identifies the optimal number of clusters, with the final model selecting 3 clusters for farmers and 3 for crop species in the ethnobiological dataset.
• Simulation studies confirm the robustness of the VEM inference strategy, showing accurate recovery of true block structures under varying network densities and cluster configurations.
• The GREMLIN R package enables full reproducibility, with simulations and real data analyses provided as interactive vignettes.
• The model outperforms standard SBM and LBM approaches in capturing complex, multi-layered interaction patterns in generalized multipartite networks.