# Robust Regression with Compositional Covariates

arXiv: https://arxiv.org/abs/1909.04990 · HTML: https://mlsanity.com/paper/1909.04990/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Sep 2019.

## Built on by (most cited first, 1 of 1)

- [Distributed Linear Regression with Compositional Covariates](https://mlsanity.com/paper/2310.13969/) (2023)

## Abstract (arXiv)

Many biological high-throughput data sets, such as targeted amplicon-based and metagenomic sequencing data, are compositional in nature. A common exploratory data analysis task is to infer statistical associations between the high-dimensional microbial compositions and habitat- or host-related covariates. We propose a general robust statistical regression framework, RobRegCC (Robust Regression with Compositional Covariates), which extends the linear log-contrast model by a mean shift formulation for capturing outliers. RobRegCC includes sparsity-promoting convex and non-convex penalties for parsimonious model estimation, a data-driven robust initialization procedure, and a novel robust cross-validation model selection scheme. We show RobRegCC's ability to perform simultaneous sparse log-contrast regression and outlier detection over a wide range of simulation settings and provide theoretical non-asymptotic guarantees for the underlying estimators. To demonstrate the seamless applicability of the workflow on real data, we consider a gut microbiome data set from HIV patients and infer robust associations between a sparse set of microbial species and host immune response from soluble CD14 measurements. All experiments are fully reproducible and available on GitHub at https://github.com/amishra-stats/robregcc.