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

成分数据，也就是对某些整体各部分的定量测量，受到限制，这就要求其分析必须有别于标准的无约束多元统计分析。高维组成数据自然出现在广泛的现代科学应用中，包括人类微生物组研究、营养科学、基因组学研究和地球化学。在这些科学应用中，由树形结构表示的层次关系通常可用于成分数据的不同组成部分。由于组成性质和树形结构，这些数据对以数据驱动的方式获得可靠和具有科学意义的见解构成了独特的挑战。目前对这种树信息组成数据的分析工作主要是为个人应用而设计的；需要在统一的框架内采用新的方法和理论。在这一需求的推动下，该项目旨在开发新的统计理论、方法和计算工具，以实现更稳健和有效的分析。该项目将为致力于统计学和其他科学领域交叉研究的学生提供跨学科的研究机会。该项目还将开发用户友好的开放源码软件，采用新的统计方法，使广大科学界受益。这个项目的目的是研究统计分析应该如何可靠和有效地考虑数据的组成性质和树结构。通过一个统一的框架，该项目将制定新颖和有原则的方法，并深入了解树形结构在了解树形结构的成分数据分析中的作用。具体地说，本研究将研究树信息成分数据分析中的三个基本问题：1)树信息成分数据的独立性和条件独立性检验；2)树信息成分数据中差异成分的测试；3)树信息成分数据的度量学习。该项目产生的方法和理论将为不同科学领域的树信息成分数据分析带来更强大和强大的实用工具，最终有助于促进科学和健康方面的知识。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.