Differential Network Analysis for Compositional Data

It is often of interest to understand how conditional dependence relationships among components of a compositional vector differs between two conditions.In this paper, we specify such a conditional dependence network among components using a compositional precision matrix.To perform differential network analysis for compositional data, we propose DNA-Coda that directly estimates the difference of two compositional precision matrices.Under mild regularity conditions, our approach is shown to be consistent in support recovery and estimation.Comprehensive simulations demonstrate DNA-Coda's statistical superiority over existing methods in the accuracy of estimation and recovery of true differential network matrix.The potential usefulness of our method is also illustrated by an application example to differential network analysis of microbiome compositional data.