Statistical Inference for Large-Scale Structured Data with Dependence and Non-Stationarity

具有相关性和非平稳性的大规模结构化数据的统计推断

• 批准号: 1712418
• 负责人: Chunming Zhang
• 金额: $ 12.5万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-08-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1712418&HistoricalAwards=false
• 关键词: Statistical; Inference; Large; Scale; Structured

This project aims to address some challenging research problems, with a common theme of exploiting spatial-temporal dependence and non-stationarity in large-scale structured data, emerging from scientific studies in biology, genetics, astronomy, economics, neuroscience, geophysics, and meteorology among others. New tools will be developed for stochastic modeling, computational algorithms, and statistical inference applied to medical imaging data such as functional magnetic resonance imaging, neuron spike trains, genome-wide association studies, and building faster file access systems. It is anticipated that these new developments will allow scientists to efficiently analyze data with significantly increased flexibility and accuracy, and thus will have direct impacts on these applications to science, public health, and information technology. The research will also be integrated with educational practice through development of a seminar course on new statistical methods for analyzing spatially and temporally correlated imaging data. The project focuses on adequate accommodation of three fundamentally different types of spatial-temporal dependence structures. The research results aim to bridge the gap between the limited theory and methodology currently available and the broad and challenging scientific problems encountered in many applied fields. Motivated by fMRI data analysis, Project 1 explores a new semi-parametric inference procedure applicable to a broad class of "non-stationary non-Gaussian temporally dependent" error processes for time-course data collected at a given spatial point. A new test statistic will be developed, and its asymptotic properties will be established. Large-scale multiple testing tasks often exhibit dependence, and accounting for the dependence among individual non-Gaussian test statistics is an important, challenging, but unsolved problem in statistics. Motivated by challenges in detection of activated brain regions from fMRI studies and assessing association between single-nucleotide polymorphisms and a disease from GWAS studies, Project 2 proposes a new multiple testing framework for a diverging number of "correlated chi-squared test statistics with an arbitrary dependence structure." Motivated by applications in multiple neural spike train recordings with dependence in both time and space, Project 3 develops new integrative methods for learning the "sparse network structured dependence" among nodes underlying a wide class of multivariate point process data with non-stationary event times.

该项目旨在解决一些具有挑战性的研究问题，其共同主题是利用大规模结构化数据中的时空依赖性和非平稳性，这些问题来自生物学，遗传学，天文学，经济学，神经科学，生物物理学和气象学等科学研究。将开发新的工具，用于随机建模，计算算法和应用于医学成像数据的统计推断，如功能性磁共振成像，神经元尖峰序列，全基因组关联研究，以及构建更快的文件访问系统。预计这些新的发展将使科学家能够有效地分析数据，并显着提高灵活性和准确性，从而将对这些应用程序产生直接影响科学，公共卫生和信息技术。该研究还将通过开发一个关于分析空间和时间相关成像数据的新统计方法的研讨会课程，与教育实践相结合。该项目的重点是充分适应三个根本不同类型的时空依赖结构。研究成果旨在弥合目前可用的有限理论和方法与许多应用领域中遇到的广泛且具有挑战性的科学问题之间的差距。受fMRI数据分析的启发，项目1探索了一种新的半参数推断程序，适用于在给定空间点收集的时程数据的广泛的“非平稳非高斯时间依赖”误差过程。将开发一个新的检验统计量，并建立其渐近性质。大规模的多测试任务往往表现出相关性，而解释单个非高斯测试统计量之间的相关性是统计学中一个重要的、具有挑战性的但尚未解决的问题。受fMRI研究中检测激活脑区和GWAS研究中评估单核苷酸多态性与疾病之间关联的挑战的启发，项目2提出了一个新的多重检验框架，用于不同数量的“具有任意依赖结构的相关卡方检验统计量”。受时间和空间依赖性的多神经尖峰序列记录应用的启发，项目3开发了新的综合方法，用于学习节点之间的“稀疏网络结构依赖性”，这些节点是一类具有非平稳事件时间的多变量点过程数据的基础。

项目成果

On simultaneous calibration of two-sample t-tests for high-dimension low-sample-size data

高维低样本数据双样本t检验的同时校准

• DOI: 10.5705/ss.202018.0467
• 发表时间: 2021
• 期刊: Statistica Sinica
• 影响因子: 1.4
• 作者: Zhang, Chunming;Jia, Shengji;Wu, Yongfeng
• 通讯作者: Wu, Yongfeng

Robust estimation in regression and classification methods for large dimensional data

• DOI: 10.1007/s10994-023-06349-2
• 发表时间: 2023-07
• 期刊: Machine Learning
• 影响因子: 7.5
• 作者: Chunming Zhang;Lixing Zhu;Yanbo Shen

Empirical likelihood inference in autoregressive models with time-varying variances

• DOI: 10.1080/24754269.2021.1913977
• 发表时间: 2021-04
• 期刊: Statistical Theory and Related Fields
• 影响因子: 0.5
• 作者: Yu Han;Chunming Zhang

Assessment of Projection Pursuit Index for Classifying High Dimension Low Sample Size Data in R

R 中高维低样本量数据分类的投影追踪指数评估

• DOI: 10.6339/23-jds1096
• 发表时间: 2023
• 期刊: Journal of Data Science
• 作者: Wu, Zhaoxing;Zhang, Chunming
• 通讯作者: Zhang, Chunming

Further Examples Related to Correlations Between Variables and Ranks

与变量和排名之间的相关性相关的更多示例

• DOI: 10.1080/00031305.2020.1831956
• 发表时间: 2021
• 期刊: The American Statistician
• 作者: Zhang, Chunming