STATISTICAL INFERENCE WITH HIGH-DIMENSIONAL DATA

高维数据的统计推断

• 批准号: 1209014
• 负责人: Cun-Hui Zhang
• 金额: $ 35.7万
• 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: 2012
• 资助国家: 美国
• 起止时间: 2012-07-01 至 2016-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1209014&HistoricalAwards=false
• 关键词: STATISTICAL; INFERENCE; DIMENSIONAL; DATA

The proposed research will develop new methodologies and algorithms for statistical inference of low-dimensional parameters with high-dimensional data. A low-dimensional projection estimator will be further developed in linear regression and extended to more general high-dimensional statistical models, including generalized linear models, the proportional hazards model, large matrix models and more. The project will investigate consistency and asymptotic normality of the proposed estimators, test of significance, confidence intervals and regions, their efficiency in terms minimum Fisher information, and their tolerance to multiplicity adjustments. This research will directly connect the fields of semi-parametric methods and high-dimensional data, producing a locally uniform and efficient framework of statistical inference. High-dimensional data is an area of intense current interest in statistical research and practice due to the rapid development of information technologies and their applications to modern scientific experiments. Important fields with an abundance of high-dimensional data include bioinformatics, signal processing, neural imaging, communications networks and more. In many such scientific and engineering applications, the number of unknowns, and thus the complexity of the problem, is a function of the number of features: genetic components in bioinformatics, brain regions or voxels in neural imaging, or computers and routers in the Internet. A longstanding challenge in high-dimensional data is statistical inference in situations where the number of features is far greater than the number of samples in the data. Existing methodologies for testing the significance of a feature commonly rely on a uniform signal strength assumption: Each feature has either no effect or an effect stronger than an inflated noise level after adjustments for the uncertainty of the set of effective features. However, this uniform signal strength assumption is, unfortunately, seldom supported by either the data or the underlying science, especially in applications in biology, medicine, and communication and social networks. The proposed research will focus on a new approach to the above mentioned longstanding problem of statistical inference with high-dimensional data. It will develop practical methods, efficient algorithms, statistical software, and solid theory for test of significance and confidence regions for low-dimensional functions of features, even when the dimension of data is high. The methodologies developed in the proposed research will be directly relevant to common applications where modern information technologies prosper.

这项拟议的研究将为高维数据的低维参数统计推断开发新的方法和算法。低维投影估计器将在线性回归中得到进一步发展，并扩展到更一般的高维统计模型，包括广义线性模型、比例风险模型、大型矩阵模型等。该项目将调查所提出的估计量的一致性和渐近正态，显著性检验，可信区间和区域，它们在最小Fisher信息方面的有效性，以及它们对多重调整的容忍度。这项研究将直接将半参数方法和高维数据领域联系起来，产生一个局部统一和高效的统计推断框架。由于信息技术的迅速发展及其在现代科学实验中的应用，高维数据是目前统计研究和实践中非常感兴趣的一个领域。具有丰富高维数据的重要领域包括生物信息学、信号处理、神经成像、通信网络等。在许多这样的科学和工程应用中，未知数的数量以及问题的复杂性是特征数量的函数：生物信息学中的遗传成分，神经成像中的大脑区域或体素，或者互联网中的计算机和路由器。高维数据中的一个长期挑战是在特征数量远远大于数据中的样本数量的情况下进行统计推断。用于测试特征重要性的现有方法通常依赖于统一的信号强度假设：在对有效特征集的不确定性进行调整之后，每个特征要么没有影响，要么具有比膨胀的噪声水平更强的影响。然而，不幸的是，这种统一的信号强度假设很少得到数据或基础科学的支持，特别是在生物学、医学、通信和社会网络的应用中。拟议的研究将集中在一种新的方法，以解决上述长期存在的高维数据统计推断问题。它将开发实用的方法、高效的算法、统计软件和坚实的理论来检验特征的低维函数的显著性和置信域，即使在数据的高维的情况下也是如此。拟议研究中制定的方法将与现代信息技术蓬勃发展的共同应用直接相关。