Novel Statistical Methods with Applications to Massive and Complex Dynamic Data

随着现代技术的出现，海量、复杂的动态数据受到越来越多的关注。海量和复杂的动态数据的例子包括单细胞RNA测序数据、功能磁共振成像数据和电子健康记录数据。然而，由于这些数据的规模和复杂性，对它们的统计分析一直是极其困难的。这一建议致力于开发一套新的统计系统和计算效率高的方法来分析海量和复杂的动态数据。拟议的项目有以下相互关联的主题。首先，PI将使用离散熵正则化最优传输来对不同类型细胞的轨迹进行建模，并开发出一种变点检测方法来推断这些细胞分化的时间。其次，PI建议为大脑动态功能连接建立时间序列模型，并检测动态变化，以帮助了解脑子区域之间的关系。第三，PI计划研究具有信息量观测的加权泛函主成分分析。这些方法将应用于电子健康记录，以进行疾病预测和因果关系发现。该提案中开发的统计方法是及时和重要的，将与许多大规模复杂的动态真实数据集相关，例如人类连接组项目和英国生物库。这项拟议的研究承诺将对遗传学和基因组学、神经科学和医学的突破性进展做出贡献，从而产生巨大的影响。本科生和研究生将接受良好的培训，帮助他们获得宝贵的技能，使他们有资格在大学、研究型医院和行业中担任有吸引力的职位。为了方便使用拟议的新方法，国际和平研究所将用R或Python语言实现这些方法，并向公众提供软件，同时出版相应的研究报告。

With the advent of modern technologies, massive and complex dynamic data have received increasing attention. Examples of massive and complex dynamic data include single-cell RNA sequencing data, functional magnetic resonance imaging data, and electronic health record data. Statistical analysis of these data, however, has been extremely difficult due to their sheer size and complexity. This proposal is devoted to developing a new set of statistically systematic and computationally efficient methods for analyzing massive and complex dynamic data. The proposed project has the following interrelated themes. First, the PI will model trajectories of different cell types using discrete entropy regularized optimal transport and develop a change point detection method to infer the time these cells differentiate. Second, the PI proposes to build time series models for brain dynamic functional connectivity and detect dynamic changes to help understand the relationship between brain subregions. Third, the PI plans to study weighted functional principal component analysis with informative observations. The methods will be applied to electronic health records for disease prediction and causal discovery. The statistical methods developed in this proposal are timely and important and will be relevant to many large-scale complex dynamic real data sets, for example, the Human Connectome Project and the UK Biobank. The proposed research promises to have a huge impact by contributing to groundbreaking advancements in genetics and genomics, neuroscience, and medical science. Undergraduate and graduate students will receive excellent training to help them to gain valuable skills that qualify them for attractive positions in universities, research hospitals, and industries. In order to facilitate the use of the proposed new methods, the PI will implement them in R or Python and make software available to the public, along with publishing the corresponding research reports.