Collaborative Research: New Statistical Methods and Theory for High-Dimensional Data

在这个大数据时代，高维数据已经变得无处不在。近年来，许多统计方法和理论被发展用于分析高维数据，并在实践中得到了成功的应用。仍有许多挑战和未决问题有待解决。他们的解决方案需要创新的想法。所提出的研究项目的动机是由真实的应用程序，目前国家的最先进的高维数据分析方法无法提供良好的解决方案。研究成果将直接应用于基因组学、医学成像、公共卫生、社交网络、电子商务等各个领域。例如，这项提案中开发的方法将使我们能够更好地了解社交网络如何演变以及大脑功能如何随着年龄的变化而变化。研究成果将通过期刊出版物、会议介绍和研讨会讲座传播。本项目的教育计划是为了培养下一代统计学家。在本项目中，提出了新的统计方法和理论，以研究大规模统计推断的三个重要课题：（a）动态图形模型和潜在图形模型，（B）含噪声和损坏数据的高维回归，（c）结构追踪中的轮廓矩阵推断。研究人员将开发创新技术来应对方法，计算和理论挑战。研究结果不仅为解决（a）、（B）和（c）中的开放问题提供了新的强大的数据分析工具，而且还揭示了从复杂高维数据中进行统计学习的一般原则。为了使研究成果随时提供给其他研究人员和从业人员，研究人员将实施本提案中开发的方法到软件包，将公开分发。

High-dimensional data have become ubiquitous in this big-data era. In recent years, many statistical methods and theory have been developed for analyzing high-dimensional data with successful applications in practice. There are still many challenges and open problems to be addressed. Their solutions call for innovative ideas. The proposed research projects are motivated by real applications where the current state-of-the-art high-dimensional data analytic methods fail to deliver good solutions. The research results will be directly applicable in various fields such as genomics, medical imaging, public health, social networks, E-commerce, and among others. For example, methods developed in this proposal will enable us to better understand how a social network evolves and how brain functions change with age. The research results will be disseminated through journal publications, conference presentations and seminar talks. This proposal has an education program that contributes to the education and training of the next-generation statisticians.In this project novel statistical methods and theory are proposed to study three important topics of large-scale statistical inference: (a) dynamic graphical models and latent graphical models, (b) high-dimensional regression with noisy and corrupted data, and (c) profile matrix inference in structural pursuit. The investigators will develop innovative techniques to handle the methodological, computational and theoretical challenges. The research results will not only provide new powerful data analytic tools for solving open problems in (a), (b) and (c), but also shed light on general principles for statistical learning from complex high-dimensional data. In order to make the research outcomes readily available to other researchers and practitioners, the investigators will implement the methodology developed in this proposal into software packages that will be publicly distributed.