Latent Network Estimation and Variable Selection for Compositional Data via Variational EM
This work addresses a specific statistical challenge in analyzing compositional data like microbiome datasets, offering a novel method for simultaneous network and covariate inference, though it is incremental in combining existing techniques for a niche domain.
The authors tackled the problem of simultaneously estimating network interactions and covariate associations for compositional count data, developing a hierarchical Bayesian model with spike-and-slab priors and a variational EM inference scheme, and demonstrated improved accuracy in network recovery through simulations and an application to microbiome data.
Network estimation and variable selection have been extensively studied in the statistical literature, but only recently have those two challenges been addressed simultaneously. In this paper, we seek to develop a novel method to simultaneously estimate network interactions and associations to relevant covariates for count data, and specifically for compositional data, which have a fixed sum constraint. We use a hierarchical Bayesian model with latent layers and employ spike-and-slab priors for both edge and covariate selection. For posterior inference, we develop a novel variational inference scheme with an expectation maximization step, to enable efficient estimation. Through simulation studies, we demonstrate that the proposed model outperforms existing methods in its accuracy of network recovery. We show the practical utility of our model via an application to microbiome data. The human microbiome has been shown to contribute to many of the functions of the human body, and also to be linked with a number of diseases. In our application, we seek to better understand the interaction between microbes and relevant covariates, as well as the interaction of microbes with each other. We provide a Python implementation of our algorithm, called SINC (Simultaneous Inference for Networks and Covariates), available online.