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

在预测因子数量明显大于观测值数量的情况下进行变量选择时，通常假设回归系数具有稀疏性，即大多数系数为零。然而，在许多实际应用中，参数的某些预定义函数是稀疏的，而不是稀疏的。这被称为广义变量选择（GVS）。具体而言，研究人员研究了GVS在功能回归、主成分分析（标准和功能）、多变量非参数回归和微阵列实验转录调控网络问题等领域的四个重要应用。研究人员在生物学、金融、制造业、市场营销、医学和物理学等统计学以外的许多领域都有直接联系。研究者认为统计学家能够，也应该在所有这些领域做出重要贡献。随着新技术的出现，如条形码扫描器和微阵列等，庞大的数据集在这些领域和许多其他领域变得越来越普遍。如此大量的数据使得开发能够产生稀疏且可解释的解决方案的统计方法变得非常重要。研究者的目标是通过自由软件包（如R）系统地开发软件来实现所提出的方法，然后使它们随时可用，并在所有这些领域中进行宣传。研究人员相信，由于他们提出的方法的解释力，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.