Personalized classification, moment selection, and time-varying networks for large-scale longitudinal data

该研究项目旨在发展新的统计理论、方法和计算算法，以解决现实世界中数据呈现出大容量、多种类和大变化速度等独特特征的问题。传统的依赖参数似然函数的方法对于高维纵向数据已不再可行。PI和她的学生打算为具有高异质性的受试者制定个性化的分类策略，并建议通过非参数随机效应估计从纵向观察中识别亚组。本研究还打算选择并优化组合高维矩条件，以降低大量矩条件的维数，同时保留数据中的重要信息，以达到估计效率。此外，还提出了一种时变网络模型，利用柔性非参数建模来处理网络结构的动态变化。该建议还寻求开发高效的计算算法来解决涉及高维参数估计和矩阵运算的优化问题。该研究项目将有助于解决统计科学中的基本问题，并将激发大量科学家在纵向/相关数据分析、分类、随机效应建模、矩选择、低秩近似和高维相关数据的时变网络等领域的兴趣。提出的研究课题在生物医学科学、基因组学、环境科学和经济学中有许多重要的应用。例如，个性化分类方法适用于个性化医疗，具有不同生物标志物的个体可以接受不同的医疗干预，以获得更有效的治疗。时变网络模型对于识别随时间变化的大脑和生物功能、社会互动和环境影响的网络关联具有强大的功能。此外，矩选择方法也适用于计量经济学中的面板数据。PI将通过开发新的专题课程，将拟议的研究领域大量纳入教育活动。该研究还将显著促进本科生和研究生的学习和训练。

This research project aims to develop new statistical theory, methods and computing algorithms to solve real world problems where the data present unique features such as large volume, large variety and large velocity of change. Traditional methods relying on parametric likelihood functions are no longer feasible for high-dimensional longitudinal data. The PI and her students intend to develop personalized classification strategies for subjects with high heterogeneity variation, and propose to identify subgroups from longitudinal observations through nonparametric random effects estimation. The proposed research also intends to select and optimally combine high-dimensional moment conditions to reduce the dimensionality of large numbers of moment conditions, while retaining the important information from the data to achieve estimation efficiency. In addition, a time-varying network model will be proposed to address dynamic changes of network structures using flexible nonparametric modeling. The proposal also seeks to develop highly efficient computational algorithms for solving optimization problems which involve high-dimensional parameter estimations and matrix operations. The proposed research project will help to tackle fundamental questions in statistical science and will stimulate interest from a large group of scientists in the fields of longitudinal/correlated data analysis, classification, random effects modeling, moment selection, low rank approximation, and time-varying networks for high-dimensional correlated data.The proposed research topics have many important applications in the biomedical sciences, genomics, environmental sciences, and economics. For example, the personalized classification method is applicable for personalized medicine, where individuals with different biomarkers can receive different medical interventions to get more effective treatment. The time-varying network model is powerful for identifying time-evolving network associations for brain and biological functions, social interaction, and environmental influence over time. In addition, the moment selection method is applicable for panel data in econometrics applications. The PI will integrate the proposed research areas substantially into educational activities through development of new topic courses. The research will also significantly advance undergraduate and graduate students' learning and training.