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

在这个大数据时代，高维数据已经无处不在。近年来，人们发展了许多分析高维数据的统计方法和理论，并在实践中得到了成功的应用。还有许多挑战和问题需要解决。他们的解决方案需要创新的想法。提出的研究项目的动机是实际应用，目前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，在这项提议中开发的方法将使我们能够更好地理解社会网络是如何演变的，以及大脑功能是如何随着年龄而变化的。研究结果将通过期刊出版物、会议演讲和研讨会演讲传播。该提案有一个教育计划，有助于下一代统计学家的教育和培训。本项目提出了新的统计方法和理论来研究大规模统计推断的三个重要主题：(a)动态图形模型和潜在图形模型，(b)带有噪声和损坏数据的高维回归，以及(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处理方法、计算和理论方面的挑战。研究结果不仅将为解决(a)、(b)和(c)中的开放性问题提供新的强大的数据分析工具，而且还将阐明从复杂高维数据中进行统计学习的一般原理。为了使其他研究人员和从业人员能够很容易地获得研究成果，研究人员将把本提案中开发的方法实施到软件包中，并将公开分发。

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.