Network Detection and Analysis Through Semi-Parametric Odds Ratio Model

这项研究的目的是开发创新的统计方法，以解决在生物系统、金融系统和社会网络等复杂系统研究中产生的海量数据分析中的挑战性问题。该项目解决了缺乏灵活的统计模型和方法来分析混合分类和连续测量的高维网络数据的问题。正在开发的方法和软件提高了网络检测、估计和解释的准确性，具有广泛的应用。其中一个这样的应用是基因组研究，它为更好地预防、诊断和治疗疾病带来了巨大的希望。该项目的网络分析方法可以揭示更准确的因果路径结构和系统功能，这反过来又可以更好地理解潜在的生物机制。该项目还为从事高维数据研究的下一代统计学家提供了培训机会。具体地说，该项目研究了在多变量数据分析中替代传统高斯模型的灵活选择。这样的数据可能是有偏抽样的，也可能包括许多离散变量，这使得数据本质上是非高斯分布的。本项目研究的半参数优势比模型统一和扩展了连续数据的高斯模型和分类数据的对数线性模型。这种方法不仅对具有高度可解释的模型参数的复杂关联进行建模，而且还自然地解决了生物医学数据收集中经常遇到的有偏抽样设计的问题。惩罚似然方法可以一致地检测混合的连续变量和离散变量(即具有混合节点的稀疏关联网络)之间的稀疏关联。将开发用于一致性稀疏网络检测的新理论和实现这些方法的算法。与传统的关联网络检测的高斯模型相比，所研究的方法具有检测变量组之间的稀疏关联的优点，而不需要对高维环境下变量组内的关联进行建模。研究成果可以大大提高从高维数据中提取信息和解释此类信息的能力。

The objective of this research is to develop innovative statistical methods for tackling the challenging problems in the analysis of massive data generated in the studies of complex systems, such as biological systems, financial systems, and social networks. This project addresses the lack of flexible statistical models and methods for the analysis of high-dimensional network data with mixed categorical and continuous measurements. The methodology and software under development increase the accuracy of the network detection, estimation, and interpretation, which have widespread applications. One such application is to genomic research that holds great promise for better disease prevention, diagnosis, and treatment. The project's approach to network analysis can reveal more accurate structures of causal pathway and system functionalities, which in turn can lead to better understand of the underlying biological mechanisms. The project also provides training opportunities for the next generation statisticians doing research on high-dimensional data.Specifically, this project studies a flexible alternative to the traditional Gaussian model in the analysis of multivariate data. Such data may be biasedly sampled and may also include many discrete variables, which makes the data inherently non-Gaussianly distributed. The semiparametric odds ratio model under study in this project unifies and extends the Gaussian models for continuous data and the log-linear model for categorical data. This approach not only models complex associations with highly interpretable model parameters, it also naturally address the problem of biased sampling designs frequently encountered in biomedical data collection. The penalized likelihood approach can consistently detect sparse associations among mixed continuous and discrete variables (i.e., sparse association networks with mixed nodes). Novel theory for consistent sparse network detection and algorithms for implementing the methods will be developed. In comparison to the traditional Gaussian model for association network detection, the methods under study have the advantages of detecting sparse association between groups of variables without modeling the association within the groups of variables in high-dimensional settings. The research results can substantially improve the information extraction from high-dimensional data and the interpretation of such information.