III: Medium: Detecting Low Dimensional Structures in Genomic Data

新的测序技术使基因组学成为一门大数据科学。这些数据具有复杂性并代表许多变量。 在试图从基因组序列中获得生物信息时，通常需要降低复杂性。有许多不同的方法可以用于计算，但由于对数据的假设，这些方法通常会引入错误。该项目将导致开发针对所收集的基因组数据类型的新方法。 这些类型的数据之一代表DNA序列，另一种来自基因表达时对序列的自然修饰。这些新方法将通过在统计框架中正确建模这些数据的独特属性，更准确地识别两种数据类型中的重要差异。该项目期间开发的方法将对基因组学领域产生重大影响，研究人员可能会发现复杂疾病的遗传基础。该项目的更广泛影响是更深入地了解复杂疾病的遗传基础，通过公共网络服务器和软件工具传播新方法用于学术研究和教育目的，并培训本科生，研究生和博士后学者。特别是，该项目将通过夏季强化计划，招募传统上在STEM领域代表性不足的少数民族，为代表性不足的群体提供培训。从高维基因组数据中发现低维结构是基因组研究中非常重要的步骤，因为该结构可以推断基因组数据中未知的混杂因素以及数据的其他重要属性，如个体的种族。目前在基因组学中常用的降维方法有很多种，但由于其对统计模型的基本假设往往在数据中被违反，因此它们可能无法从基因组数据中生成准确的低维结构。本项目提出了针对基因组数据，特别是甲基化和基因型数据的降维方法。这些方法将结合基因组数据中存在的独特性质，例如基因型数据的离散性质和相关结构，以及不同细胞类型和组织中的不同甲基化模式。本计画亦将利用随机矩阵理论分析新方法的渐近行为。三种策略将被用来验证的方法。 首先，对于所有基因组学应用，存在具有金标准信息的数据集，其次，基于基因组学社区当前实践的模拟数据将用于执行评估基因组学应用。 例如，通过结合来自参考数据集（如1000个基因组项目）的已知祖先的个体的基因型来模拟混合个体的遗传学是社区中的标准。 第三，该团队将通过使用各种生成模型生成模拟数据来评估通用算法，以验证算法具有预期的渐近行为，并检查这些算法在违反其假设时的表现。 该方法将有助于统计领域的改进目前的低维方法和基因组学领域的软件工具发布。该项目更广泛的影响是更深入地了解复杂疾病的遗传基础，通过公共网络服务器和软件工具传播用于学术研究和教育目的的方法，并培训本科生，研究生和博士后学者。特别是，该项目将为代表性不足的群体提供夏季强化计划，招募传统上在STEM领域代表性不足的少数民族。

New sequencing technologies have made genomics a big data science. These data have complexity and represent many variables. In trying to get biological information from genomic sequence, it is often necessary to reduce the complexity. There are a number of different approaches to use computationally, but these often introduce errors because of assumptions made about the data. This project will lead to the development of novel approaches specific to the type of genomic data collected. One of these types of data represents the DNA sequence and the other comes from natural modifications to the sequence when genes are expressed. These new methods will identify important differences more accurately in the two data types by correctly modeling unique properties of these data in a statistical framework. Methods developed during this project will have a great impact on the genomics field, where researchers may discover the genetic basis of complex diseases. The broader impacts of this project are gaining a deeper insight into the genetic basis of complex diseases, distributing the novel methods through public webservers and software tools for academic research and educational purposes, and training undergraduate students, graduate students, and postdoctoral scholars. In particular, this project will provide training to underrepresented groups with a summer intensive program that recruits minorities traditionally underrepresented in STEM fields.Discovering a low dimensional structure from the high dimensional genomic data is a very important procedure in genomic studies because this structure may infer unknown confounding factors in genomic data as well as other important properties of data such as ethnicity of individuals. There are several dimensionality reduction methods prevalently used in the genomics, they may not generate an accurate low dimensional structure from genomic data because their underlying assumption on the statistical model is often violated in the data. This project proposes to develop dimensionality reduction methods aimed for genomic data, especially for methylation and genotype data. These methods will incorporate unique properties present in genomic data such as the discrete nature and correlation structure of genotype data, and different methylation patterns across different cell types and tissues. This project will also analyze asymptotic behavior of the novel methods using random matrix theory. Three strategies will be used to validate the methods. First, for all genomics applications, there are datasets where there is gold standard information, Second, simulated data based on current practices in the genomics community will be used to perform evaluate genomics applications. For example, it is standard in the community to simulate the genetics of admixed individuals by combining the genotypes of individuals of known ancestry from a reference dataset such as the 1000 Genomes project. Third, the team will evaluate the general algorithms by generating simulated data using various generative models to validate that the algorithms have the asymptotic behavior expected and also examine how these algorithms perform when their assumptions are violated. The methods will contribute both to the statistical field by improving current low dimensionality methods and to the genomics field by releasing software tools. The broader impacts of this project are gaining a deeper insight into the genetic basis of complex diseases, distributing the methods through public webservers and software tools for academic research and educational purposes, and training undergraduate students, graduate students, and postdoctoral scholars. In particular, this project will provide training to underrepresented groups with a summer intensive program that recruits minorities traditionally underrepresented in STEM fields.