Nonparametric Inference and Prediction for Complex Data by Data Depth, Confidence Distribution and Monte Carlo Method

通过数据深度、置信分布和蒙特卡罗方法对复杂数据进行非参数推理和预测

• 批准号: 1812048
• 负责人: Regina Liu
• 金额: $ 15万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-08-15 至 2022-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1812048&HistoricalAwards=false
• 关键词: Nonparametric; Inference; Prediction; Complex; Data

In the era of information and data explosion, the demand of effective data analysis methods for solving problems and assisting decision-making has never been greater. This demand comes from all domains, from modern scientific endeavors, government and industry policy-making, financial and business strategic planning, to even the most basic social-economic studies. Despite recent great strides made in mathematical and statistical sciences, many new challenges have been brought to the fore by the need of confronting the pervasive massive, diverse and complex data. The PIs of this project will develop several novel approaches to addresses general inference and prediction problems in settings where data sources are diverse or where the conventional statistical large sample theory fails to apply.Motivated by several real applications, this project will develop nonparametric approaches for: individualized inference from diverse data sources (referring to as i-Fusion), prediction for complex data, and exact inference for estimating equations. Underlying these proposed approaches is the common tool kit consisting of data depth, confidence distribution and Monte Carlo methods. The proposed approaches are expected to be broadly applicable, efficient and computationally feasible. Three specific projects are: A. Develop the new i-Fusion for drawing efficient individualized inference by effectively combining learnings from relevant data sources; B. Develop CD Monte-Carlo methods for the exact inference for estimating equations; C. Develop nonparametric predictive distributions for efficient prediction with complex data. The proposed methodologies will be developed with theoretical support and applied to the areas: i) prediction of volumes of application submissions to interrelated units in a government agency; and ii) performance forecast for individual companies by borrowing information possibly shared by others, and, potentially, iii) identification of hot spots in tracking glacial striation around the globe. These applications are motivated by the PIs' ongoing collaborative projects with the CCICADA of Department of Homeland Security, and possibly Rutgers Climate Risk and Resilience Initiative. These projects involve real databases and are ideally suited for engaging and training students and new researchers.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.

在信息和数据爆炸的时代，对解决问题和辅助决策的有效数据分析方法的需求从未如此之大。这种需求来自各个领域，从现代科学研究，政府和行业决策，金融和商业战略规划，甚至是最基本的社会经济研究。尽管最近在数学和统计科学方面取得了很大的进步，但由于需要面对无处不在的大量，多样和复杂的数据，许多新的挑战已经摆在了面前。本项目的PI将开发几种新颖的方法来解决数据源多样化或传统统计大样本理论无法应用的情况下的一般推断和预测问题。受几个真实的应用的启发，本项目将开发非参数方法：来自不同数据源的个性化推断（称为i-Fusion）、复杂数据的预测以及用于估计方程的精确推断。这些方法的基础是由数据深度、置信度分布和蒙特卡罗方法组成的通用工具包。所提出的方法是广泛适用的，有效的和计算上可行的。三个具体项目是：A.开发新的i-Fusion，通过有效地结合相关数据源的学习，进行有效的个性化推理; B.发展CD蒙特-卡罗方法，用于精确推断估计方程;开发非参数预测分布，以便对复杂数据进行有效预测。所提出的方法将在理论支持下开发，并应用于以下领域：i）预测向政府机构相关单位提交的申请数量; ii）通过借用其他公司可能共享的信息对单个公司进行业绩预测; iii）确定跟踪地球仪周围冰川条纹的热点。这些申请是由PI与国土安全部CCICADA正在进行的合作项目推动的，可能还有罗格斯大学的气候风险和复原力倡议。这些项目涉及真实的数据库，非常适合吸引和培训学生和新研究人员。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响力进行评估，被认为值得支持。审查标准。

项目成果

Discussion of Professor Bradley Efron’s Article on “Prediction, Estimation, and Attribution”

Bradley Efron 教授关于“预测、估计和归因”的文章的讨论

• DOI: 10.1111/insr.12415
• 发表时间: 2020
• 期刊: International Statistical Review
• 影响因子: 2
• 作者: Xie, Min‐ge;Zheng, Zheshi
• 通讯作者: Zheng, Zheshi

Individualized Group Learning

• DOI: 10.1080/01621459.2021.1947306
• 发表时间: 2019-06
• 期刊: Journal of the American Statistical Association
• 影响因子: 3.7
• 作者: Chencheng Cai;Rong Chen;Min‐ge Xie

Leveraging the Fisher Randomization Test using Confidence Distributions: Inference, Combination and Fusion Learning

利用置信分布的 Fisher 随机化检验：推理、组合和融合学习

• DOI: 10.1111/rssb.12429
• 发表时间: 2021
• 期刊: Journal of the Royal Statistical Society Series B: Statistical Methodology
• 作者: Luo, Xiaokang;Dasgupta, Tirthankar;Xie, Minge;Liu, Regina Y.
• 通讯作者: Liu, Regina Y.

Nonparametric predictive distributions based on conformal prediction

• DOI: 10.1007/s10994-018-5755-8
• 发表时间: 2019-03-01
• 期刊: MACHINE LEARNING
• 影响因子: 7.5
• 作者: Vovk, Vladimir;Shen, Jieli;Xie, Min-ge
• 通讯作者: Xie, Min-ge

Nonparametric Fusion Learning for Multiparameters: Synthesize Inferences From Diverse Sources Using Data Depth and Confidence Distribution

多参数的非参数融合学习：使用数据深度和置信分布从不同来源综合推论

• DOI: 10.1080/01621459.2021.1902817
• 发表时间: 2021
• 期刊: Journal of the American Statistical Association
• 影响因子: 3.7
• 作者: Liu, Dungang;Liu, Regina Y.;Xie, Min-ge
• 通讯作者: Xie, Min-ge