Collaborative Research: Semiparametric Conditional Graphical Models with Applications to Gene Network Analysis

本课题的研究工作是基于以下问题展开的。在许多遗传学研究中，除了基因表达数据外，其他类型的数据都是从相同的个体中收集的。问题是如何在构建基因网络时利用这些额外的信息。研究人员通过条件高斯图形模型(CGGM)来描述这一问题，在该模型中，外部变量被并入作为预测变量。他们提出了一种结合再生核Hilbert空间和套索型正则化的模型估计方法。前者用于构造条件协方差矩阵的无模型估计，后者用于推导条件精度矩阵的稀疏估计，其零进入模式对应于描述基因网络的图。他们建议研究该模型的渐近性质，介绍确定调谐常数的方法，并为该模型开发标准化和可公开访问的计算机程序。此外，调查人员建议从两个方向扩展CGGM。首先，他们建议放松高斯假设，对残差应用Copula变换，然后使用伪似然估计条件相关性。然后对它们进行套索型正则化，以产生精度矩阵的稀疏估计器。第二个方向是发展足够的图形模型，这是一种同时降低预测者的维度和估计响应的图形结构的机制。高通量技术使研究人员能够在基因组水平上收集和监测信息，在过去的15年里已经彻底改变了生物学领域。这些数据提供了前所未有的数量和类型多样的数据，揭示了生物过程的不同方面。同时，它们也提出了许多传统统计方法无法解决的统计和计算挑战。在目前的基因组学研究中，基于单个基因的统计分析可能会导致正在研究的生物过程的信息丢失，这一点已经变得越来越明显。例如，一项关于识别糖尿病患者遗传模式的广为人知的研究表明，没有一个单一基因能在统计学上突出表明导致这些模式的原因，但当对基因进行分组分析时，就出现了明确的信号。在这一观察的推动下，基因网络受到了更多的关注。研究人员提出了一类新的统计方法，称为条件图形模型，用于构建可以考虑一组协变量的基因网络。他们还计划为所提出的方法开发理论性质和计算机程序。尽管他们的研究始于基因网络，但研究人员预计，条件图形模型将在基因组学之外有更广泛的应用，比如预测资产回报和研究社交网络，这些在这个互联网时代变得越来越普遍。

The research proposed in this project is motivated by the following problem. In many genetic studies, in addition to gene expression data, other types f data are collected from the same individuals. The problem is how to make use of this additional information when construct gene networks. The investigators formulate this problem by a conditional Gaussian graphical model (CGGM), in which the external variables are incorporated as predictors. They propose an estimation procedure for this model by combining reproducing kernel Hilbert space with the lasso type regularization. The former is used to construct a model-free estimate of the conditional covariance matrix, and the latter is used to derive a sparse estimators of the conditional precision matrix, whose zero entry pattern correspond to a graph that describes the gene network. They propose to study the asymptotic properties, to introduce methods to determine the tuning constants, and to develop standardized and openly accessible computer programs for this model. Furthermore, the investigators propose to extend the CGGM in two directions. First, they propose to relax the Gaussian assumption by applying a copula transformation to the residuals and then using pseudo likelihood to estimate conditional correlations. These are then subject to the lasso-type regularization to yield sparse estimator of the precision matrix. The second direction is the development of sufficient graphical model, which is a mechanism to simultaneously reduce the dimension of the predictor and estimate the graphical structure of the response.High-throughput technologies that enable researchers to collect and monitor information at the genome level have revolutionized the field of biology in the past fifteen years. These data offer unprecedented amount and diverse types of data that reveal different aspects of the biological processes. At the same time, they also present many statistical and computational challenges that cannot be addressed by traditional statistical methods. In current genomics research it has become increasingly clear that statistical analysis based on individual genes may incur loss of information on the biological process under study. For example, a widely known study on identifying genetic patterns of diabetic patients show that no single gene could stand out statistically as responsible for the patterns, and yet clear signals emerged when genes were analyzed in groups. Motivated by this observation, greater attention has been paid to networks of genes. The investigators propose a class of new statistical methods, called conditional graphical models, for constructing gene networks that can take into account of a set of covariates. They also plan to develop theoretical properties and computer programs for the proposed methods. Although their inquire began with gene networks, the investigators envision conditional graphical models to have broad applications beyond genomics, such as in predicting asset returns and in studying social networks, which are becoming all the more prevalent in this age of Internet.