Collaborative Research: Semiparametric conditional graphical models with applications to gene network analysis

合作研究：半参数条件图模型及其在基因网络分析中的应用

• 批准号: 1106738
• 负责人: Hongyu Zhao
• 金额: $ 8万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1106738&HistoricalAwards=false
• 关键词: Collaborative; Research; Semiparametric; conditional; graphical

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.

本项目提出的研究是出于以下问题。在许多遗传学研究中，除了基因表达数据外，还从同一个体收集其他类型的数据。问题是在构建基因网络时如何利用这些附加信息。研究人员通过条件高斯图模型（CGGM）来阐述这个问题，其中外部变量被纳入作为预测变量。他们通过将再生核希尔伯特空间与套索类型正则化相结合，提出了该模型的估计过程。前者用于构造条件协方差矩阵的无模型估计，后者用于导出条件精度矩阵的稀疏估计量，其零条目模式对应于描述基因网络的图。他们建议研究渐近性质，引入确定调整常数的方法，并为此模型开发标准化且可公开访问的计算机程序。此外，研究人员建议将 CGGM 向两个方向扩展。首先，他们建议通过对残差应用联结变换来放松高斯假设，然后使用伪似然来估计条件相关性。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。第二个方向是开发足够的图形模型，这是一种同时减少预测变量维度和估计响应图形结构的机制。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，在过去十五年里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不同类型的数据，揭示了生物过程的不同方面。同时，它们还提出了许多传统统计方法无法解决的统计和计算挑战。在当前的基因组学研究中，越来越清楚的是，基于个体基因的统计分析可能会导致所研究的生物过程的信息丢失。例如，一项广为人知的关于识别糖尿病患者遗传模式的研究表明，没有任何一个基因能够在统计学上脱颖而出，对这些模式负责，但当对基因进行分组分析时，会出现清晰的信号。受这一观察的推动，基因网络受到了更多关注。研究人员提出了一类新的统计方法，称为条件图模型，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特性和计算机程序。尽管他们的研究始于基因网络，但研究人员设想条件图形模型具有基因组学之外的广泛应用，例如预测资产回报和研究社交网络，这些在互联网时代变得越来越普遍。