High Dimensional Methods for Complex Data Refining

回归分析的目的是研究输入变量X和输出变量Y之间的关系。当参数模型未知，而变量数量又很大时，就会出现困难。降维方法克服这些困难已经被许多作者研究。为了在一个共同的屋顶下拥抱降维的许多方面，提出了一个新的论坛，称为Z介导的方法。在这种设置中，除了输入和输出变量之外，还引入了第三组变量Z，它扮演了调解X和Y之间关系变化的角色。通常，Z变量的数量远大于X或Y变量的数量。但只有一小部分Z变量可能有真实的影响。将构造新的方法来降低X，Y和Z的维数。在生命科学中，对处理大型数据集（如来自微阵列和医学成像的数据集）的需求呈爆炸性增长之际，出现了一波尖端统计活动。该提议的动机来自于复杂基因调控的动态视角，其中两个功能相关的基因X和Y可能由第三个未知基因Z介导。挑战在于如何仅基于微阵列数据识别候选基因Z的短列表。这里开发的方法可用于阐明疾病，基因和代谢途径之间的相互作用，从而有助于药物发现和造福社会。调查结果不仅将通过标准出版物传播，而且还将通过建立一个网站供公众查阅。还提供了学生在生物信息学工作的跨学科培训。

Regression analysis aims at the study of the relationship between input variables X and out variables Y. Difficulties occur when no parametric model is known, and yet the number of variables is large. Dimension reduction methods for overcoming such difficulties have been investigated by many authors. To embrace many aspects of dimension reduction under one common roof, a new forum called the Z-mediated approach is proposed. In this setting, in addition to the input and out variables, a third group of variables Z is introduced, which fills the role of mediating the change in the relationship between X and Y. Typically the number of Z variables is much larger than the number of X or Y variables. But only a small portion of Z variables may have a real influence. New methods will be constructed to reduce the dimension of X, Y and Z. A wave of cutting-edge statistical activities have arrived at a time when there is an explosive demand for processing large data sets in the life sciences, such as those from microarrays and medical imaging. The motivation of this proposal comes from a dynamic perspective about complex gene regulation where two functionally associated genes X and Y may be mediated by a third unknown gene Z. The challenge is how to identify a short list of candidate gene Z based on microarray data alone. The methodology developed here can be used for elucidating the interplay between disease, genes, and metabolic pathways, thus contributing to drug discovery and benefiting society. The results will be disseminated not only via standard publication, but also by constructing a website for public access. Interdisciplinary training of students to work in bioinformatics is also provided.