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

当在预测器的数量明显大于观测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，事实证明，在许多实际应用中，参数的某些预定义函数是稀疏的，而不是参数稀疏的。这称为广义变量选择(GVS)。具体地说，研究人员研究了GVS在功能回归、主成分分析(标准和功能)、多元非参数回归以及基因芯片实验转录调控网络问题等领域的四个重要应用，研究人员在生物、金融、制造、营销、医学和物理等统计学之外的许多领域都有直接的联系。调查人员认为，统计学家可以而且应该在所有这些领域做出重要贡献。随着条形码扫描仪和微阵列等新技术的出现，海量数据集在这些领域和许多其他领域变得越来越常见。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重要。研究人员的目标是系统地开发软件，通过R等自由软件包实施所提出的方法，然后使它们随时可用，并在所有这些领域宣传它们。调查人员相信，由于他们提出的方法具有解释力，一旦该软件可用，它将得到广泛应用。

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.