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

在这个大数据时代，高维数据变得无处不在。近年来，人们发展了许多用于高维数据分析的统计方法和理论，并在实践中得到了成功的应用。仍然有许多挑战和悬而未决的问题需要解决。他们的解决方案需要创新的想法。建议的研究项目是由实际应用驱动的，在这些应用中，当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，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是如何演变的，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、会议报告和研讨会演讲进行传播。在这项计划中，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)含噪声和受污染数据的高维回归；(C)结构追踪中的剖面矩阵推理。研究人员将开发创新技术，以应对方法、计算和理论上的挑战。研究结果不仅将为解决(A)、(B)和(C)中的公开问题提供新的强大的数据分析工具，而且还将揭示从复杂的高维数据中进行统计学习的一般原则。为了使其他研究人员和从业人员容易地获得研究成果，调查人员将把本提案中开发的方法应用到将公开分发的软件包中。

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.