Theory and Methods for Tree-Informed High-Dimensional Compositional Data Analysis

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

Compositional data, that is, quantitative measurements of the parts of some whole, is subject to constraints that necessitate its analysis be distinct from that of standard unconstrained multivariate statistical analysis. High-dimensional compositional data naturally arises in a wide range of modern scientific applications, including human microbiome studies, nutritional science, genomics studies, and geochemistry. In these scientific applications, a hierarchical relationship represented by a tree structure is often available for the compositional data’s different components. Because of compositional nature and tree structure, these data pose a unique challenge to gaining reliable and scientifically meaningful insights in a data-driven way. Current efforts on analyzing such tree-informed compositional data are primarily designed for individual applications; there is need for new methodology and theory in a unified framework. Motivated by this need, this project aims to develop novel statistical theories, methodologies, and computational tools for more robust and efficient analysis. The project will provide interdisciplinary research opportunities for students who aim to work on the intersection between statistics and other scientific areas. The project will also develop user-friendly open-source software implementing the new statistical methods to benefit a broad scientific community. This project aims to study how statistical analysis should take data's compositional nature and tree structure into account reliably and efficiently. Through a unified framework, the project will develop novel and principled methodologies and provide a deep understanding of the tree structure's role in tree-informed compositional data analysis. Specifically, this research will study three fundamental topics in tree-informed compositional data analysis: 1) independence and conditional independence test for tree-informed compositional data, 2) testing for differential components in tree-informed compositional data, and 3) metric learning for tree-informed compositional data. The resulting methods and theories from the project will lead to more robust and powerful practical tools for tree-informed compositional data analysis in different scientific fields, ultimately helping advance knowledge in science and health. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.