# Inference for microbe–metabolite association networks using a latent graph model

## TL;DR

This paper introduces a new method to better detect relationships between microbes and metabolites in biological networks.

## Contribution

A novel inference procedure using a bipartite stochastic block model to enhance power and control false discovery rates in microbe-metabolite networks.

## Key findings

- The proposed method improves detection of significant associations in microbe-metabolite networks.
- The approach clusters microbes and metabolites into modules for better interpretation.
- The method was validated through simulations and applied to bacterial vaginosis data.

## Abstract

Correlation networks are commonly used to infer associations between microbes and metabolites. The resulting \documentclass[12pt]{minimal}
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$p$\end{document}-values are then corrected for multiple comparisons using existing methods such as the Benjamini & Hochberg (BH) procedure to control the false discovery rate (FDR). However, most existing methods for FDR control assume the \documentclass[12pt]{minimal}
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$p$\end{document}-values are weakly dependent. Consequently, they can have low power in recovering microbe–metabolite association networks that exhibit important topological features, such as the presence of densely associated modules. We propose a novel inference procedure that is both powerful for detecting significant associations in the microbe–metabolite network and capable of controlling the FDR. Power enhancement is achieved by modeling latent structures in the form of a bipartite stochastic block model. We develop a variational expectation–maximization (EM) algorithm to estimate the model parameters and incorporate the learned graph in the testing procedure. In addition to FDR control, this procedure provides a clustering of microbes and metabolites into modules, which is useful for interpretation. We demonstrate the merit of the proposed method in simulations and an application to bacterial vaginosis.