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，用于衡量变量重要性和选择高维生物数据中的关键变量。这项研究的两个主要组成部分是基于距离的多个维度的程序和基于倾斜/加权的任何特定维度的重要性衡量标准。基于距离的方法，例如多响应置换过程和距离协方差，即使在维度数目大于样本大小的情况下也提供处理数据的能力。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评估任何维度的变量重要性。因此，变量重要性是在多变量背景下评估的，而不是在单变量边缘分布上评估。此外，新方法将允许所选变量的数量超过样本量；允许前向选择、后向选择和稀疏惩罚加权；最小化对数据中实际存在的相关性结构的扰动；需要最小的结构假设；对广泛的多变量相关性敏感，包括一些难以甚至不可能用现有方法检测到的相关性。作为该项目的一部分开发的方法在生物医学和农业行业有广泛的应用。现代基因组学工具允许研究人员同时测量数千个变量，这些变量包含有关生物体的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。在包括药物发现、遗传风险分析、个性化药物以及动植物育种在内的各种领域，发现这种关联是至关重要的。这项研究项目将提供工具，帮助这些发现成为可能。新方法的可靠软件实施将被创建、维护、存档在公共存储库中，并免费分发给基因组学研究人员和从事各种生物体和不同高通量技术的行业从业者。这项研究活动将加强计算/统计领域和实验/生物医学领域的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.