Analysis of High Dimensional Compositional Data Containing Structural Zeros with Applications to Microbiome Data

2016/05/20 by Abhishek Kaul, Kaul, Abhishek, Ori Davidov +3
Computer Science · Engineering · #Applications (stat.AP) #FOS: Biological sciences #FOS: Computer and information sciences #Geochemistry and Geologic Mapping #Hydrocarbon exploration and reservoir analysis #Quantitative Methods (q-bio.QM)

paper · pdf · doi:10.48550/arxiv.1605.06193

openalex publication_date 2016/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is motivated by the recent interest in the analysis of high dimen- sional microbiome data. A key feature of this data is the presence of `structural zeros' which are microbes missing from an observation vector due to an underlying biological process and not due to error in measurement. Typical notions of missingness are insufficient to model these structural zeros. We define a general framework which allows for structural zeros in the model and propose methods of estimating sparse high dimensional covariance and precision matrices under this setup. We establish error bounds in the spectral and frobenius norms for the proposed esti- mators and empirically support them with a simulation study. We also apply the proposed methodology to the global human gut microbiome data of Yatsunenko (2012).

Related

• CARE: Large Precision Matrix Estimation for Compositional Data
• Geometry-preserving and interpretable dimension reduction for compositional data
• Robust Covariance Estimation for High-dimensional Compositional Data with Application to Microbial Communities Analysis
• MarZIC: A Marginal mediation model for Zero-Inflated Compositional mediators with applications to microbiome data
• It's All Relative: New Regression Paradigm for Microbiome Compositional Data