Matrix variate modeling and analysis of large scale biological data with complex dependencies

矩阵变量模型提供了一种分析复杂多变量数据集的方法，其中变量和观测单位之间可能存在有意义的关系。这是多变量统计分析更标准设置的延伸，其中变量是相关的，但观察结果被视为独立的。将数据作为单个高维样本处理的主要动机是，在估计对实验单元之间关系敏感的参数时，可能会增加功率。高维非渐近理论、凸分析和算法的最新进展使这些模型能够适合于基因组学和神经科学等关键科学领域中出现的非常大的数据集。该项目的一个主要目标是评估在多大程度上对样本之间的关系进行核算，以便对变量之间的关系作出更准确的估计。如何应用这种方法的一个例子是评估罕见遗传变异和表型之间的关联。序列核关联测试（SKAT）使用核矩阵，核矩阵本质上是遗传特征的协方差矩阵。研究人员将评估从最近提出的Gemini方法获得的协方差矩阵作为SKAT程序的核心进行矩阵变量分析。已经确定了双子框架可以有效扩展到的三个科学应用。除了概念和算法方面的挑战外，这些应用还需要Gemini估计器的理论和方法来覆盖新的设置，例如，由于SNP基因型高度非高斯，以及由于大脑连接图随时间变化。研究人员将使基线双子座模型和算法适应这些新的设置，并研究它们的统计和计算特性。最近在仪器方面的技术突破使描述生命系统的大量详细数据集得以有效收集。生物学和健康科学领域的研究人员已经接受了这些技术，但有时会因为这样的数据必须被保守地解释，以防止做出不可重复的声明而感到沮丧。如果有可能以一种提供更多统计能力的方式分析这些数据，而不需要昂贵地增加样本量，研究进展将会加快。实现这一目标的一个途径是超越独立对待研究中观察单位（例如人类研究对象或实验动物）的范式。研究者和他的同事们开发了一种新型的统计程序，利用观察单位之间的推断关系来更准确地估计物理和生物上的未知因素。他们计划开发技术背后的理论，开发执行分析的软件，并与癌症生物学、基因组学和神经科学领域的科学家合作，评估使用这种方法获得新的科学见解的潜力。该项目将重点关注三个科学问题：识别与癌症发生和进展有关的DNA病变，识别与人类疾病相关的遗传基因变异，以及表征意识状态变化引起的神经连通性变化。

Matrix-variate models provide a way to analyze complex multivariate datasets in which meaningful relationships may exist among both the variables and among the observed units. This is an extension of the more standard setting of multivariate statistical analysis, in which the variables are dependent, but the observations are viewed as being independent. The primary motivation for treating the data as a single high-dimensional sample is the potential for increased power when estimating parameters that are sensitive to relationships among the experimental units. Recent advances in high-dimensional non-asymptotic theory, convex analysis, and algorithms allow such models to be fit to the very large data sets that arise in critical scientific areas such as genomics and neuroscience. A major goal of this project is to assess the extent to which accounting for relationships among samples allows more accurate estimates to be made of relationships among variables. An example of how this might be applied is in the assessment of associations between rare genetic variants and a phenotype. The Sequential Kernel Association Test (SKAT) uses a kernel matrix which is essentially a covariance matrix of the genetic features. The investigators will evaluate the use of the covariance matrix obtained from the recently-proposed Gemini approach to matrix-variate analysis as a kernel for the SKAT procedure. Three scientific applications have been identified to which the Gemini framework may be usefully extended. In addition to conceptual and algorithmic challenges, these applications require the theory and methodology for the Gemini estimators to cover new settings, for example, due to SNP genotypes being highly non-Gaussian, and due to brain connectivity graphs changing over time. The investigators will adapt the baseline Gemini models and algorithms to these new settings, and study their statistical and computational properties.Recent technological breakthroughs in instrumentation allow large and detailed data sets describing living systems to be efficiently collected. Researchers in biology and health science have embraced these technologies, but have sometimes been frustrated by the fact that such data must be interpreted conservatively, to guard against making non-reproducible claims. Research progress would be accelerated if it were possible to analyze such data in a way that provides more statistical power, without expensive increases in the sample size. One path to doing this is to move beyond the paradigm of treating the observed units in a study (e.g. human research subjects or laboratory animals) independently. The investigator and his colleagues have developed a new type of statistical procedure that uses inferred relationships among the units of observation to more accurately estimate physical and biological unknowns. They plan to develop the theory behind their technique, to develop software for carrying out the analyses, and to work with scientists in cancer biology, genomics, and neuroscience to assess the potential for using this approach to obtain novel scientific insights. The project will focus on three scientific problems: identification of DNA lesions involved with cancer incidence and progression, identification of inherited genetic variants associated with human diseases, and characterization of neural connectivity changes induced by changes in consciousness state.