Collaborative Research: Generalized Variable Selection With Applications To Functional Data Analysis And Other Problems

University Of Southern California, Los Angeles CA

Investigators

Abstract

When variable selection is performed in situations where the number of predictors is significantly larger than the number of observations, one generally assumes sparsity in the regression coefficients, i.e., most of the coefficients are zero. However, there turn out to be many practical applications where, rather than the parameters being sparse, certain predefined functions of the parameters are sparse. This is referred to as "Generalized Variable Selection" (GVS). Specifically, the investigators study four important applications of GVS in areas as diverse as functional regression, principal component analysis (both standard and functional), multivariate non-parametric regression, and transcription regulation network problems for microarray experiments. The investigators have direct connections in many fields outside statistics such as Biology, Finance, Manufacturing, Marketing, Medicine and Physics. The investigators believe that statisticians can, and should, make important contributions in all these areas. With the advent of new technologies, such as bar code scanners and microarrays etc., enormous data sets are becoming increasingly common in these and many other fields. Such vast quantities of data have made it important to develop statistical methodologies that can produce sparse and interpretable solutions. The investigators aim to systematically develop software to implement the proposed methods through free software packages, like R, and then make them readily available and publicize them in all these fields. The investigators believe that, because of the interpretive power of their proposed methods, once the software is available, it will be widely utilized.