III: Small: Randomized Matrix-Sketching Approaches for the Analysis of Massive Human Genomics Data

人类遗传学的研究人员现在可以获得前所未有的大量遗传信息，这些信息描述了我们彼此之间的真正差异。从计算机科学和应用数学的角度来看，所得到的数据集可以被认为是矩阵，行代表个体，列代表基因组中与常见或罕见多态性相对应的基因座。通过分析这些数据集，全基因组关联研究（GWAS）报告了遗传变异和复杂性状之间超过10，000种强关联。然而，允许非常大规模数据集的有效分析的工具仍然缺失。从这些数据集中提取有用的信息，促进了科学的进步，同时也促进了公共健康、繁荣和福利。本项目将弥合理论计算机科学领域开发的最先进算法与将这些算法应用于分析人类遗传学领域日益庞大的数据集之间的差距。本项目将从理论和实践的角度探讨如何使用随机线性代数来加速人类遗传学数据分析。第一个研究方向将研究线性混合模型或LIFE：LIFE形成对感兴趣表型的遗传效应的线性模型。随机线性代数工具将用于加速优化问题的解决方案，而不会牺牲精度。第二个研究方向将研究多基因风险评分（PRS），其通常通过首先使用单标记显著性检验从所有可用标记（通常为数百万）中选择大量遗传标记（通常为数万）来操作。该特征选择阶段之后是在所选标记上构建回归模型以预测表型。随机线性代数工具将用于加快PRS方法，同时保持泛化精度。最后，第三个研究方向，将探索如何利用群体遗传学数据集的特定结构，以设计改进的随机线性代数工具来分析人类遗传学数据集。研究人员将把他们的结果传播给广泛的应用数学家、理论计算机科学家和人口遗传学家。他们都参加人口遗传学会议和研讨会，并在人口遗传学的知名期刊上发表文章，以及在计算机科学的会议和研讨会上发表文章。研究人员还将向毕业生和本科生传播这些知识。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Researchers in human genetics have now access to unprecedented amounts of genetic information characterizing how truly different we are from one another. From a Computer Science and Applied Mathematics perspective, the resulting datasets can be thought of as matrices, with the rows representing individuals and the columns representing loci in the genome that correspond to common or rare polymorphisms. Analyzing such datasets, Genome Wide Association Studies (GWAS) have reported over 10,000 strong associations between genetic variants and complex traits. However, tools that allow efficient analysis of very large scale datasets are still missing. Extracting useful information from such datasets promotes the progress of science and, at the same time, advances public health, prosperity, and welfare. This project will bridge the gap between state-of-the-art algorithms developed in the theoretical computer science community and the application of such algorithms to the analysis of the increasingly larger volume of datasets in the human genetics community.This project will explore how randomized linear algebra, from a theoretical and practical standpoint, can be used to speed human genetics data analytics. The first research direction will investigate Linear Mixed Models or LMMs: LMMs form a linear model of the genetic effects on the phenotype of interest. Randomized linear algebra tools will be used to speed up the solution of the resulting optimization problem, without sacrificing accuracy. The second research direction will investigate Polygenic Risk Scores (PRS), which typically operate by first selecting a large number of genetic markers (often in the tens of thousands) out of all available markers (often in the many millions) using single marker significance tests. This feature selection stage is followed by building regression models on the selected markers to predict phenotypes. Randomized linear algebra tools will be used to speed up PRS approaches, while preserving generalization accuracy. Finally, the third research direction, will explore how the particular structure of population genetics datasets can be leveraged in order to design improved randomized linear algebra tools for the analysis of human genetics datasets. The investigators will disseminate their results to a broad community of applied mathematicians, theoretical computer scientists, and population geneticists. They both participate in population genetics conferences and workshops and publish in high-profile journals in population genetics, as well as in conferences and workshops in Computer Science. The investigators will additionally disseminate this knowledge to graduates and undergraduates. They will involve under-represented groups in their research activities, leveraging their prior track record of involving such groups in cutting-edge research.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.