In this paper we consider the computational problem of inferring K microbial networks from a given sample-taxa matrix. We recently proposed a mixture model framework to address this problem, where the taxa counts in each of the K components is modeled using a Multivariate Poisson Log-Normal (MPLN) distribution, and such that the precision matrix of the distribution associated with each mixture component defines a separate microbial network. The parameters of our mixture model (MixMPLN) were estimated in a maximum likelihood framework setting, and our optimization algorithm was based on the Minorization-Maximization (MM) principle combined with gradient ascent and block updates. Here, we extend the application of the MM framework to propose two new algorithms for inferring K microbial networks from a sample-taxa matrix. The first algorithm, MixGGM, applies a log-ratio transform to the sample-taxa count matrix and subsequently models the problem as a mixture of Multivariate Gaussian distributions. The second algorithm, MixMCMC, is based on the MixMPLN formulation but estimates a subset of the mixture parameters using a Markov Chain Monte Carlo (MCMC) sampling strategy rather than by direct optimization. We also extend these algorithms to address the inference of sparse networks. We evaluate the performances of the three methods (MixMPLN, MixMCMC, and MixGGM) on synthetic datasets generated from a comprehensive collection of graph types (band, cluster, scale-free, and random). We also applied MixMPLN and MixGGM to a real dataset. The code and datasets are available on https://github.com/sahatava/MicNet.

MOTIVATION: The interactions among the constituent members of a microbial community play a major role in determining the overall behavior of the community and the abundance levels of its members. These interactions can be modeled using a network whose nodes represent microbial taxa and edges represent pairwise interactions. A microbial network is typically constructed from a sample-taxa count matrix that is obtained by sequencing multiple biological samples and identifying taxa counts. From large-scale microbiome studies, it is evident that microbial community compositions and interactions are impacted by environmental and/or host factors. Thus, it is not unreasonable to expect that a sample-taxa matrix generated as part of a large study involving multiple environmental or clinical parameters can be associated with more than one microbial network. However, to our knowledge, microbial network inference methods proposed thus far assume that the sample-taxa matrix is associated with a single network. RESULTS: We present a mixture model framework to address the scenario when the sample-taxa matrix is associated with K microbial networks. This count matrix is modeled using a mixture of K Multivariate Poisson Log-Normal distributions and parameters are estimated using a maximum likelihood framework. Our parameter estimation algorithm is based on the minorization-maximization principle combined with gradient ascent and block updates. Synthetic datasets were generated to assess the performance of our approach on absolute count data, compositional data and normalized data. We also addressed the recovery of sparse networks based on an l1-penalty model. AVAILABILITY AND IMPLEMENTATION: MixMPLN is implemented in R and is freely available at https://github.com/sahatava/MixMPLN. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.