Direct interaction network and differential network inference from compositional data via lasso penalized D-trace loss

The development of high-throughput sequencing technologies for 16S rRNA gene profiling provides higher quality compositional data for microbe communities. Inferring the direct interaction network under a specific condition and understanding how the network structure changes between two different environmental or genetic conditions are two important topics in biological studies. However, the compositional nature and high dimensionality of the data are challenging in the context of network and differential network recovery. To address this problem in the present paper, we proposed two new loss functions to incorporate the data transformations developed for compositional data analysis into D-trace loss for network and differential network estimation, respectively. The sparse matrix estimators are defined as the minimizer of the corresponding lasso penalized loss. Our method is characterized by its straightforward application based on the ADMM algorithm for numerical solution. Simulations show that the proposed method outperforms other state-of-the-art methods in network and differential network inference under different scenarios. Finally, as an illustration, our method is applied to a mouse skin microbiome data.