Statistical Modeling with High-dimensional Data: Variable Selection and Regularization

对于高维数据，简约模型是首选，因为它们更容易解释，同时减少预测误差。正则化也是大多数现代数据分析发展中的重要组成部分，特别是在预测因子数量很大的情况下。非正则化的拟合肯定会产生严重的过度拟合和无用的模型。研究人员对高维统计建模中的变量选择问题采取了正则化的方法，使得所得到的模型具有良好的预测精度，同时具有稀疏表示。具体地说，研究人员开发了：(1)蛋白质组学数据分析中的新的融合变量选择方法，这是一种革命性的癌症诊断工具；(2)一种新的核Logistic回归模型，它自动采用支持向量表示；(3)在估计多分位数回归函数时执行同时变量选择的几种新技术。研究人员还研究了这些新的变量选择技术的理论。高效的算法和软件是为公众使用而开发的。现代科学创新使科学家能够收集海量和高维数据。在科学研究中，从海量数据中提取有用的信息是至关重要的。因此，变量选择和降维在高维统计建模中起着基础性的作用。变量选择问题出现在广泛的领域，例如机器学习、药物发现、生物标记物发现、遗传学、蛋白质组学、脑成像分析、金融建模、环境科学等。该研究项目旨在开发最先进的统计工具，帮助各个领域的研究人员分析他们的数据。

With high-dimensional data parsimonious models are preferred because they are much more interpretable and at the same time reduce prediction errors. Regularization is also an essential component in most modern developments for data analysis, in particular when the number of predictors is large. Non-regularized fitting is guaranteed to give badly over-fitted and useless models. The investigators take a regularization approach to the variable selection problem in high-dimensional statistical modeling such that the resulting model enjoys excellent prediction accuracy and at the same time has a sparse representation. In particular, the investigators develop: (1) new fused variable selection methods in proteomics data analysis which has been arevolutionary cancer diagnostic tool; (2) a novel kernel logistic regression model which automatically adopts a support-vector representation; (3) several new techniques for performing simultaneous variable selection in estimating multiple quantile regression functions. The investigators also study the theory of these new variable selection techniques. Efficient algorithms and software are developed for public use.Modern scientific innovations allow scientists to collect massive and high-dimensional data. It is critical in scientific investigations to extract useful information from the huge amount of data. For this reason, variable selection and dimension reduction play a fundamental role in high-dimensional statistical modeling. Variable selection problems arise from a wide range of fields, machine learning, drug discovery, biomarker finding, genetics, proteomics, brain imaging analysis, financial modeling, environmental sciences, to name a few. The research project aims to develop state-of-the-art statistical tools that help researchers in various fields to analyze their data.