III: Small: Novel Statistical Data Analysis Approaches for Mining Human Genetics Datasets

现代基因分型和测序技术的出现彻底改变了人类遗传学研究，使研究人员能够真正了解我们彼此之间的差异。描述人类遗传变异的常见模式的大型数据集可以很容易地被认为是矩阵，行代表个体，列代表基因组中与常见多态性相对应的基因座。这些数据集的更广泛的影响怎么强调都不过分：它们是研究人员用来寻找影响健康，疾病以及对药物和环境因素的反应的基因的关键资源，以及了解我们物种的进化和生物历史。从这些数据集中提取有用的信息可以促进科学的进步，同时促进国家的健康，繁荣和福利。该项目将弥合理论计算机科学和应用数学领域开发的最先进的数据分析算法与人类遗传学领域越来越大的数据集分析的应用之间的差距。在该项目的背景下，首先，从算法的角度来看，项目团队将设计和分析三个原型的新颖算法，结合了联合收割机线性代数和随机化的基础研究课题，即稀疏主成分分析、矩阵完备化和线性（或核）判别分析。所有这三个主题在理论计算机科学、机器学习和应用数学社区都很受欢迎。然而，这些研究课题基本上被群体遗传学界所忽视。其次，从群体遗传学的角度来看，该团队将应用开发的算法获得有关群体结构、血统信息标记和自然选择的新见解，并改进插补方法和全基因组关联研究（GWAS）数据分析。所有三种方法都将在PI可用的群体遗传学数据集上进行评价。该项目将培训研究生，并将研究成果传播给应用数学家，理论计算机科学家和人口遗传学家的广泛社区。

The advent of modern genotyping and sequencing technologies has revolutionized human genetics research, allowing researchers to truly understand how different we are from one another. Large datasets describing the common patterns of human genetic variation may be easily thought of as matrices, with the rows representing individuals and the columns representing loci in the genome that correspond to common polymorphisms. The broader impact of such datasets cannot be overemphasized: they are a key resource for researchers to use to find genes affecting health, disease, and responses to drugs and environmental factors, as well as understanding the evolutionary and biological history of our species. Extracting useful information from such datasets promotes the progress of science and, at the same time, advances national health, prosperity and welfare. This project will bridge the gap between state-of-the-art algorithms for data analysis developed in the theoretical computer science and applied mathematics communities and the application of such algorithms to the analysis of the increasingly larger volume of datasets in the human genetics community.In the context of this project, first, from an algorithmic perspective, the project team will design and analyze novel algorithms for three prototypical, fundamental research topics that combine linear algebra and randomization, namely sparse Principal Components Analysis, matrix completion, and linear (or kernel) discriminant analysis. All three topics have been widely popular in the theoretical computer science, machine learning, and applied mathematics communities. Yet these research topics have been essentially overlooked by the population genetics community. Second, from a population genetics perspective, the team will apply the developed algorithms to gain novel insights regarding population structure, ancestry informative markers, and natural selection, as well as improve imputation methods and Genome-Wide Association Studies (GWAS) data analysis. All three methods will be evaluated on population genetics datasets that are available to the PIs. The project will train graduate students and will disseminate the results of the research to a broad community of applied mathematicians, theoretical computer scientists, and population geneticists.