# High-dimensional Log-Error-in-Variable Regression with Applications to Microbial Compositional Data Analysis

arXiv: https://arxiv.org/abs/1811.11709 · HTML: https://mlsanity.com/paper/1811.11709/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Nov 2018.

## Built on by (most cited first, 4 of 4)

- [Instrumental Variable Estimation for Compositional Treatments](https://mlsanity.com/paper/2106.11234/) (2021)
- [Tensor Decomposition with Unaligned Observations](https://mlsanity.com/paper/2410.14046/) (2024)
- [CARE: Large Precision Matrix Estimation for Compositional Data](https://mlsanity.com/paper/2309.06985/) (2023)
- [Debiased high-dimensional regression calibration for errors-in-variables log-contrast models](https://mlsanity.com/paper/2409.07568/) (2024)

## Abstract (arXiv)

In microbiome and genomic studies, the regression of compositional data has been a crucial tool for identifying microbial taxa or genes that are associated with clinical phenotypes. To account for the variation in sequencing depth, the classic log-contrast model is often used where read counts are normalized into compositions. However, zero read counts and the randomness in covariates remain critical issues. In this article, we introduce a surprisingly simple, interpretable, and efficient method for the estimation of compositional data regression through the lens of a novel high-dimensional log-error-in-variable regression model. The proposed method provides both corrections on sequencing data with possible overdispersion and simultaneously avoids any subjective imputation of zero read counts. We provide theoretical justifications with matching upper and lower bounds for the estimation error. The merit of the procedure is illustrated through real data analysis and simulation studies.