Abstract

Compositional data represent the relative abundances of individual

components within a whole and arise in a wide range of scientific fields.

A

central task in compositional data analysis is to characterize conditional dependence among components, typically through estimation of the precision matrix

in graphical models. Most existing methods are designed for a single compositional vector. In microbiome studies, however, multiple compositional vectors

— such as bacterial and fungal profiles — are often observed for each sample,

posing additional challenges for network inference. In particular, precision matrix estimation is complicated by compositional constraints, high dimensionality

and the need to jointly model multiple interdependent compositional vectors. In

this paper, we propose an adaptive procedure, called Amcoda, for estimating

the precision matrix of latent absolute abundances from multiple compositional

vectors. We establish convergence rates for the Amcoda estimator under various matrix norms and provide theoretical guarantees for support recovery. Ex-

tensive simulations demonstrate that Amcoda outperforms existing methods in

both estimation accuracy and edge detection for network inference from multiple

compositional vectors. We further apply Amcoda to a real microbiome dataset

to infer bacterial-fungal cross-domain networks and identify several interactions

of potential biological interest.

Key words and phrases: Compositional data analysis, graphical models, high- dimensional inference, microbiome networks, precision matrix estimation

Information

Preprint No.SS-2026-0002
Manuscript IDSS-2026-0002
Complete AuthorsShen Zhang, Huaying Fang, Tao Hu
Corresponding AuthorsHuaying Fang
Emailshyfang@cnu.edu.cn

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Acknowledgments

This work was supported by the Beijing Outstanding Young Scientist Program [JWZQ20240101027], the Beijing Natural Science Foundation [JR25003]

and the National Natural Science Foundation of China [12101425, 12171328].

Supplementary Materials

Proofs of all theoretical results and additional simulation studies are provided in the Supplementary Material.

Supplementary materials are available for download.