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CAREER: Modernizing Classical Nonparametric and Multivariate Theory for Large-scale, High-dimensional Data Analysis

职业：现代化经典非参数和多元理论以进行大规模、高维数据分析

基本信息

批准号：
1553884
负责人：
Jing Lei
金额：
$ 40万
依托单位：
Carnegie-Mellon University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2016
资助国家：
美国
起止时间：
2016-08-01 至 2021-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1553884&HistoricalAwards=false
关键词：
CAREER Modernizing Classical Nonparametric Multivariate

项目摘要

The constantly increasing dimensionality and complexity of modern data has motivated many new data analysis tools in various fields, and urgently call for rigorous theoretical investigation, such as robustness against different sources of model misspecification,uncertainty quantification in classification and prediction, and statistical performance guarantee of conventional methods under non-standard settings. Although most classical theory are not directly applicable to methods developed for complex data, partially due to highly specialized model assumptions and diversified algorithms, the profound statistical thinking carried in these long-established results can still provide deep theoretical insights. When combined with cutting-edge results in modern context such as random matrix theory, matrix concentration, and convex geometry, these classical theory will lead to novel principled methods for a general class of problems ranging from high dimensional regression and classification to network data analysis and subspace learning. All methods developed in the proposed research will be implemented as standard R packages freely available and will have high pedagogical value and will be used to develop new courses. The proposed research has applications in astronomy and medical screening data. The proposal also provides new inference tools for applied areas in genetics, psychiatry, brain sciences. Integrated educational activities include designing courses on new perspectives in nonparametric statistics and modern multivariate analysis.The proposed work will further integrate classical nonparametric and multivariate analysis theory with modern elements in four major areas of statistical research, including assumption-free prediction bands in high dimensional regression; a generalized Neyman-Pearson framework for set-valued multi-class classification; statistical performance guarantee of some greedy algorithms in network community detection as well as goodness-of-fit tests for network model selection; and a unified singular value decomposition framework for structured subspace estimation formulated as a convex optimization problem. These research activities will lead to modernized nonparametric and multivariate analysis courses, featuring new theoretical frameworks such as computationally constrained minimax analysis, additional topics such as functional data analysis, and cutting-edge examples in genetics, brain imaging, traffic, and astronomy.

现代数据的不断增加的维度和复杂性促使各个领域出现了许多新的数据分析工具，迫切需要进行严格的理论研究，如对模型误指定的不同来源的稳健性，分类和预测的不确定性量化，以及传统方法在非标准设置下的统计性能保证。尽管大多数经典理论不能直接适用于为复杂数据开发的方法，部分原因是高度专业化的模型假设和多样化的算法，但这些长期确立的结果中蕴含的深刻统计思想仍然可以提供深刻的理论见解。当与现代背景下的前沿结果(如随机矩阵理论、矩阵集中和凸几何)相结合时，这些经典理论将导致针对从高维回归和分类到网络数据分析和子空间学习的一类一般问题的新的原则性方法。拟议研究中开发的所有方法都将作为免费提供的标准R包实施，将具有很高的教学价值，并将用于开发新课程。这项拟议的研究在天文学和医学筛查数据中有应用。该提案还为遗传学、精神病学、脑科学等应用领域提供了新的推理工具。综合教育活动包括设计关于非参数统计和现代多元分析的新视角的课程。拟议的工作将进一步将经典的非参数和多元分析理论与统计研究的四个主要领域的现代元素相结合，包括高维回归中的无假设预测带；集值多类分类的广义Neyman-Pearson框架；网络社区检测中一些贪婪算法的统计性能保证以及网络模型选择的拟合优度检验；以及作为凸优化问题的结构化子空间估计的统一奇异值分解框架。这些研究活动将导致现代化的非参数和多元分析课程，以新的理论框架为特色，如计算受限的极小极大分析，额外的主题，如函数数据分析，以及遗传学、脑成像、交通和天文学的前沿例子。