Rank-based Inference for Complex and Noisy High-dimensional Data

该研究项目将开发一套统一的统计，计算和软件工具，以解决复杂和嘈杂的高维数据分析中的数据挖掘和发现科学挑战。具有这些特征的数据在许多领域都很常见，包括健康科学、经济学、金融和神经科学。然而，分析这些类型数据的统计方法并没有跟上新技术和新数据集的发展。该项目将开发强大的数据分析方法，可扩展到大型复杂数据集。最大限度地减少高维、数据复杂性和噪声对数据分析的影响的能力将促进健康和经济等重要领域的新发现。该项目将进行理论和实证研究。将分发公开提供的软件，以补充研究活动。该研究员将指导统计学和社会科学的研究生，并将寻求扩大代表性不足的群体的参与。该项目将开发基于多变量排名的方法，这些方法对模型错误指定，离群值，缺失值和数据依赖性具有鲁棒性。与复杂和嘈杂的高维数据的基于秩的推理相关的三个问题将得到解决。首先，将开发用于稳健功能主成分分析的基于多变量秩的统计方法。这些新的方法将改善目前的功能主成分分析工具的噪声数据，并将被应用到身体活动数据的分析。该项目的部分动机是对复杂和嘈杂的股票市场和神经影像数据的研究，该项目将设计基于多变量等级的依赖性测量作为测量组间依赖性的新量化。新的量化将同时纳入非线性相关性测量，测试的一致性，鲁棒性和分布自由。在第二项活动的基础上，该项目将通过基于多变量等级的依赖性措施来评估组级网络，以表征条件而不是边缘独立结构。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智力价值和更广泛的影响审查标准进行评估来支持。

This research project will develop a unified set of statistical, computational, and software tools to address data mining and discovery science challenges in the analysis of complex and noisy high-dimensional data. Data with these characteristics are common in many fields, including the health sciences, economics, finance, and neuroscience. However, statistical methods to analyze these types of data have not kept up with the development of new technologies and new datasets. This project will develop robust data analysis methods that are scalable to large complex datasets. The ability to minimize the impact of high dimensionality, data complexity, and noisiness on data analysis will facilitate new discoveries in important areas such as health and economics. The project will conduct both theoretical and empirical studies. Publicly available software will be disseminated to complement the research activities. The investigator will mentor graduate students in statistics and social sciences and will seek to broaden the participation of underrepresented groups.This project will develop multivariate rank-based methods that are robust to model misspecification, outliers, missing values, and data dependency. Three problems associated with rank-based inference for complex and noisy high-dimensional data will be addressed. First, multivariate rank-based statistical methods for robust functional principal component analysis will be developed. These new methods will improve on current functional principal component analysis tools for noisy data and will be applied to the analysis of physical activity data. Motivated in part by studies of complex and noisy stock market and neuroimaging data, the project will devise multivariate rank-based dependence measures as new quantifications for measuring between-group dependences. The new quantifications will simultaneously incorporate nonlinear dependence measurement, consistency of testing, robustness, and distribution-freeness. Building on the second activity, the project will estimate group-level networks through multivariate rank-based dependence measures to characterize conditional instead of marginal independence structure.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.