CDS&E: Graph-Based Learning and Uncertainty Quantification for Large-Scale Complex Data

许多现代经验和实验研究经常产生大量的高维和复杂的数据。图模型是可视化和挖掘高维复杂数据中隐藏的、潜在的、低维结构的重要工具之一。受神经科学和基因组学应用的启发，该研究项目旨在开发基于计算和统计方法的尖端图形模型，以揭示大规模复杂数据中的潜在网络结构。为了提高科学研究的可重复性，该项目提供了严格的不确定性量化工具。将开发软件包来实施所提出的方法。该研究项目侧重于神经科学和基因组学应用中高维复杂数据的图形模型的理论和方法发展。具体项目包括提出基于聚类的大量变量降维潜变量模型、通信约束下海量异构数据的最优分布式学习与推理、复杂依赖下高维纵向数据的指数族随机效应图模型等。所提出的模型配备了一个强大的多重测试程序，以严格的方式控制错误发现率。该奖项反映了NSF的法定使命，并被认为是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的支持。

Many modern empirical and experimental researches routinely produce massive amounts of high-dimensional and complex data. Graphical model is one of the most important tools to visualize and exploit hidden, latent, low-dimensional structure in high-dimensional complex data. Motivated by neuroscience and genomics applications, the research project aims to develop cutting-edge graphical model based computational and statistical methods to uncover latent network structures in large-scale complex data. To enhance the reproducibility of scientific studies, the project provides rigorous tools on uncertainty quantification. The software packages will be developed to implement the proposed methods. The research project focuses on theoretical and methodological development for graphical models in high-dimensional complex data arising from neuroscience and genomics applications. Specific projects include proposing clustering based latent variable models for dimensional reduction with a large number of variables, optimal distributed learning and inference for massive heterogenous data under communication constraint, and exponential family random effect graphical models for high-dimensional longitudinal data under complex dependence. The proposed models are equipped with a powerful multiple testing procedure to control false discovery rate in a rigorous manner. The computational algorithms will be developed in each application.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.