Model Selection for Sparse Microbial Network Inference Using Variational Approximation.

Microbial communities are often composed of taxa from different taxonomic groups. The associations among the constituent members in a microbial community play an important role in determining the functional characteristics of the community, and these associations can be modeled using an edge weighted graph (microbial network). A microbial network is typically inferred from a sample-taxa matrix that is obtained by sequencing multiple biological samples and identifying the taxa abundance in each sample. Motivated by microbiome studies that involve a large number of samples collected across a range of study parameters, here we consider the computational problem of identifying the number of microbial networks underlying the observed sample-taxa abundance matrix. Specifically, we consider the problem of determing the number of sparse microbial networks in this setting. We use a mixture model framework to address this problem, and present formulations to model both count data and proportion data. We propose several variational approximation based algorithms that allow the incorporation of the sparsity constraint while estimating the number of components in the mixture model. We evaluate these algorithms on a large number of simulated datasets generated using a collection of different graph structures (band, hub, cluster, random, and scale-free).