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

当在预测因子的数量显著大于观测值的数量的情况下执行变量选择时，通常假设回归系数中的稀疏性，即，大多数系数为零。然而，在许多实际应用中，参数不是稀疏的，而是参数的某些预定义函数是稀疏的。这被称为广义变量选择（GVS）。具体来说，研究人员研究了GVS在不同领域的四个重要应用，如函数回归，主成分分析（标准和函数），多元非参数回归，以及微阵列实验的转录调控网络问题。研究人员在统计学之外的许多领域，如生物学，金融，制造业，市场营销，医学和物理学都有直接联系。调查人员认为，统计人员能够而且应该在所有这些领域作出重要贡献。随着新技术的出现，如条形码扫描仪和微阵列等，在这些领域和许多其它领域中，庞大的数据集正变得越来越普遍。如此大量的数据使得开发能够产生稀疏和可解释的解决方案的统计方法变得非常重要。研究人员的目标是系统地开发软件，通过自由软件包（如R）实现所提出的方法，然后使它们随时可用，并在所有这些领域推广。研究人员认为，由于他们提出的方法的解释能力，一旦软件可用，它将被广泛使用。

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.