Abstract

High-dimensional compositional regression is common in microbiome studies, where covariates are

relative abundances and the number of taxa often exceeds the sample size. Standard regression methods

may be invalid for such data. While the centered log-ratio transformed linear model offers a principled

framework, it yields unstable estimates with limited target samples.

We develop transfer learning

procedures that borrow information from auxiliary source studies for high-dimensional compositional

regression with subcomposition structures and additional non-compositional covariates. The proposed

methods incorporate the compositional linear constraint through constrained ℓ1 -regularized estimation

and allow both model and covariate shifts across studies. We propose Oracle-Trans-sub-Coda-Lasso,

for known informative sources, and Trans-sub-Coda-Lasso, which detects informative sources using

marginal screening statistics.

Under suitable regularity and similarity conditions, we establish the

ℓ2-norm error convergence rate of the oracle estimator and the consistency of the source-detection

procedure. Simulations and an application to ulcerative colitis gut microbiome data for body mass

index prediction demonstrate the improved performance of the proposed methods.

Key words and phrases: Transfer learning, Multisource data, Compositional data, Centered log-ratio model, High-dimensional regression

Information

Preprint No.SS-2025-0314
Manuscript IDSS-2025-0314
Complete AuthorsQinqin Hu, Xiaojing Luo, Chencheng Ma, Wang Zhou
Corresponding AuthorsQinqin Hu
Emailsqqhu@sdu.edu.cn

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Acknowledgments

The authors wish to thank the Co-Editor, the Associate Editor and three reviewers for

their many helpful and insightful comments and suggestions that greatly improved the paper. This work was supported in part by Shandong Provincial Natural Science Foundation

Supplementary Materials

The Supplementary Material includes the following sections: S1, the details of Algorithm

1S2, proof for the theorem 1; S3, proof for the theorem 2; S4, additional comparison with

other constrained methods; S5, additional results of our numerical studies and real studies.

Supplementary materials are available for download.