Flexible Statistical Modelling for High Dimensional Data

高维数据的灵活统计建模

• 批准号: 1915842
• 负责人: Hui Zou
• 金额: $ 17.95万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-09-01 至 2023-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1915842&HistoricalAwards=false
• 关键词: Flexible; Statistical; Modelling; Dimensional; Data

Scientific and technology innovations have made massive high-dimensional data ubiquitous in various fields, such as biological science, medical studies, public health, social sciences, e-commerce, finance, climate studies, and so on. During the past decade statisticians have developed a rich collection of new tools for high-dimensional statistical modeling. Despite these important advances, there are still many challenges and open problems to be dealt with in high-dimensional data analysis. Their solutions require innovative ideas and techniques to handle the methodological, computational and theoretical challenges. The goal of this research is to develop mathematically solid and computationally efficient methods to address these pressing and important inferential challenges. This research consists of three projects. The first project concerns measurement errors in high-dimensional M-estimation. The PI will study a new unified convex approach to solve the error-in-variables penalized M-regression including Huber regression, logistic regression, quantile regression, and the support vector machine. In the second project the PI will establish a new inference tool named composite M-estimation and demonstrate its applications in high-dimensional learning. In the third project the PI will study a flexible heterogeneity pursuit method for understanding the heterogeneity effects in high-dimensional data. Software packages will be created to make the new methods readily available to other researchers and practitioners.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

随着科学技术的发展，高维数据在生物科学、医学研究、公共卫生、社会科学、电子商务、金融、气候研究等各个领域中无处不在，统计学家们在过去的十年中开发了大量的高维统计建模工具。尽管有这些重要的进展，仍然有许多挑战和开放的问题要处理在高维数据分析。他们的解决方案需要创新的想法和技术来应对方法，计算和理论挑战。这项研究的目标是开发数学上可靠和计算效率高的方法来解决这些紧迫和重要的推理挑战。本研究包括三个项目。第一个项目涉及高维M-估计中的测量误差。PI将研究一种新的统一凸方法来解决变量中的错误惩罚M-回归，包括Huber回归，逻辑回归，分位数回归和支持向量机。在第二个项目中，PI将建立一个新的推理工具，称为复合M-估计，并展示其在高维学习中的应用。在第三个项目中，PI将研究一种灵活的异质性追踪方法，用于理解高维数据中的异质性效应。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。

项目成果

Expectile regression via deep residual networks

• DOI: 10.1002/sta4.315
• 发表时间: 2020-09
• 期刊: Stat
• 影响因子: 1.7
• 作者: Yiyi Yin;H. Zou

Fast and Exact Leave-One-Out Analysis of Large-Margin Classifiers

大余量分类器的快速准确留一分析

• DOI: 10.1080/00401706.2021.1967199
• 发表时间: 2022
• 期刊: Technometrics
• 影响因子: 2.5
• 作者: Wang, Boxiang;Zou, Hui
• 通讯作者: Zou, Hui

Sparse Composite Quantile Regression in Ultrahigh Dimensions With Tuning Parameter Calibration

• DOI: 10.1109/tit.2020.3001090
• 发表时间: 2020-11-01
• 期刊: IEEE TRANSACTIONS ON INFORMATION THEORY
• 影响因子: 2.5
• 作者: Gu, Yuwen;Zou, Hui
• 通讯作者: Zou, Hui

Exactly Uncorrelated Sparse Principal Component Analysis

完全不相关的稀疏主成分分析

• DOI: 10.1080/10618600.2023.2232843
• 发表时间: 2023
• 期刊: Journal of Computational and Graphical Statistics
• 影响因子: 2.4
• 作者: Kwon, Oh-Ran;Lu, Zhaosong;Zou, Hui
• 通讯作者: Zou, Hui

A simple method to improve principal components regression

• DOI: 10.1002/sta4.288
• 发表时间: 2020-01-01
• 期刊: STAT
• 影响因子: 1.7
• 作者: Lang, Wenjun;Zou, Hui
• 通讯作者: Zou, Hui