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

在这个项目中提出的研究是由以下问题驱动的。在许多基因研究中，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。研究人员通过一个条件高斯图形模型（CGGM）来阐述这个问题，其中外部变量被纳入预测因子。他们将核希尔伯特空间的再现与lasso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，其零入口模式对应于描述基因网络的图。他们建议研究渐近性质，引入确定调谐常数的方法，并为该模型开发标准化和开放的计算机程序。此外，研究人员建议将CGGM扩展到两个方向。首先，他们提出通过对残差进行copula变换来放宽高斯假设，然后使用伪似然来估计条件相关性。然后对其进行lasso型正则化，得到精度矩阵的稀疏估计量。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器维数和估计响应的图形结构的机制。在过去的15年里，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，这给生物学领域带来了革命性的变化。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。与此同时，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，越来越明显的是，基于个体基因的统计分析可能会导致所研究的生物过程信息的丢失。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，没有一个基因可以在统计上脱颖而出，对这些模式负责，然而，当对基因进行分组分析时，清晰的信号出现了。受到这一观察结果的启发，人们对基因网络给予了更多的关注。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。他们还计划为提出的方法开发理论性质和计算机程序。虽然他们的研究是从基因网络开始的，但研究人员设想条件图形模型在基因组学之外有广泛的应用，比如预测资产回报和研究在这个互联网时代变得越来越普遍的社交网络。

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.