Distance-based variable selection for high-dimensional biological data

该研究项目的总体目标是为统计学家和生物科学家提供新的和改进的统计工具，用于测量变量的重要性和选择高维生物数据中的关键变量。 该研究的两个主要组成部分是跨多个维度的基于距离的程序和任何特定维度的基于倾斜/加权的重要性度量。基于距离的方法，例如，多响应置换过程和距离协方差提供了处理数据的能力，即使维数大于样本大小。 基于倾斜/加权的程序允许在存在任何数量的其他变量的情况下针对任何维度评估变量重要性。因此，变量的重要性是在多变量的背景下，而不是单变量的边际分布进行评估。 此外，新的方法将允许选择的变量的数量超过样本大小;允许向前选择，向后选择和稀疏惩罚加权;最大限度地减少对数据中实际存在的相关结构的扰动;需要最少的结构假设;并且对大范围的多变量依赖性敏感，包括一些用现有方法很难甚至不可能检测到的。作为本项目一部分开发的方法在生物医学和农业行业有广泛的应用。 现代基因组学工具使研究人员能够同时测量数千个变量，这些变量包含有关生物体DNA，RNA和蛋白质特征的信息。 必须挖掘这些现代高通量技术产生的高维数据，以确定与健康结果或其他重要特征最相关的变量。 揭示这种关联在许多领域都至关重要，包括药物发现，遗传风险分析，个性化医疗以及植物和动物育种。这项研究项目将提供工具，帮助使这些发现成为可能。 新方法的可靠软件实现将被创建、维护、存档在公共存储库中，并免费传播给基因组学研究人员和从事各种生物和不同高通量技术工作的行业从业者。 研究活动将加强计算/统计领域和实验/生物医学领域研究人员之间的合作和伙伴关系。

The overall objective of the research project is to provide statisticians and biological scientists new and improved statistical tools for measuring variable importance and selecting key variables in high-dimensional biological data. The two major ingredients underlying the research are a distance-based procedure across multiple dimensions and a tilting/weighting-based importance measure for any specific dimension. The distance-based methods, e.g., the multi-response permutation procedure and the distance covariance, provide the ability to handle data even if the number of dimensions is larger than the sample size. The tilting/weighting-based procedures allow variable importance to be evaluated for any dimension in the presence of any number of other variables. Thus, variable importance is evaluated in the multivariate context rather than on univariate marginal distributions. In addition, the new methods will allow the number of selected variables to exceed the sample size; allow forward selection, backward selection, and sparse penalized weighting; minimize perturbation to the dependence structures actually present in the data; require minimal structural assumptions; and be sensitive to a wide range of multivariate dependencies, including some difficult or even impossible to detect with existing methods.The methods developed as part of this project have a wide range of applications in biomedical and agricultural industries. Modern genomics tools allow researchers to simultaneously measure thousands of variables that contain information about DNA, RNA, and protein characteristics of organisms. The high-dimensional data generated by these modern high-throughput technologies must be mined to identify the variables that are most associated with health outcomes or other important traits. Uncovering of such associations is crucial in a variety of areas including drug discovery, genetic risk analysis, personalized medicine, and plant and animal breeding. This research project will provide tools to help make these discoveries possible. Reliable software implementations of the new methods will be created, maintained, archived in public repositories, and freely disseminated to genomics researchers and industry practitioners working with a diverse range of organisms and different high-throughput technologies. The research activity will enhance collaborations and partnerships among researchers from both computational/statistical fields and experimental/biomedical fields.