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Network estimation and variable selection have been extensively studied inthe statistical literature, but only recently have those two challenges beenaddressed simultaneously. In this paper, we seek to develop a novel method tosimultaneously estimate network interactions and associations to relevantcovariates for count data, and specifically for compositional data, which havea fixed sum constraint. We use a hierarchical Bayesian model with latent layersand employ spike-and-slab priors for both edge and covariate selection. Forposterior inference, we develop a novel variational inference scheme with anexpectation maximization step, to enable efficient estimation. Throughsimulation studies, we demonstrate that the proposed model outperforms existingmethods in its accuracy of network recovery. We show the practical utility ofour model via an application to microbiome data. The human microbiome has beenshown to contribute to many of the functions of the human body, and also to belinked with a number of diseases. In our application, we seek to betterunderstand the interaction between microbes and relevant covariates, as well asthe interaction of microbes with each other. We provide a Python implementationof our algorithm, called SINC (Simultaneous Inference for Networks andCovariates), available online.

Latent Network Estimation and Variable Selection for Compositional Data via Variational EM