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.
