Scalable estimation of microbial co-occurrence networks with Variational Autoencoders

Estimating microbe-microbe interactions is critical for understanding the ecological laws governing microbial communities. Rapidly decreasing sequencing costs have promised new opportunities to estimate microbe-microbe interactions across thousands of uncultured, unknown microbes. However, typical microbiome datasets are very high dimensional and accurate estimation of microbial correlations requires tens of thousands of samples, exceeding the computational capabilities of existing methodologies. Furthermore, the vast majority of microbiome studies collect compositional metagenomics data which enforces a negative bias when computing microbe-microbe correlations. The Multinomial Logistic Normal (MLN) distribution has been shown to be effective at inferring microbe-microbe correlations, however scalable Bayesian inference of these distributions has remained elusive. Here, we show that carefully constructed Variational Autoencoders (VAEs) augmented with the Isometric Log-ratio (ILR) transform can estimate low-rank MLN distributions thousands of times faster than existing methods. These VAEs can be trained on tens of thousands of samples, enabling co-occurrence inference across tens of thousands of microbes without regularization. The latent embedding distances computed from these VAEs are competitive with existing beta-diversity methods across a variety of mouse and human microbiome classification and regression tasks, with notable improvements on longitudinal studies.