New Tools for Large-Scale Sparse Inference

在许多应用领域，高通量设备使人们能够在很短的时间内收集数千甚至有时数百万个测量值。该研究项目解决了脑成像、基因组学和遗传学以及社交网络等大数据领域产生的统计问题。该研究包括几个部分：(a)收集和清理社交网络的大规模数据集；(b)开发分析大型社会网络的新模型、方法和理论；(c)开发新的方法和理论来分析基因组和遗传数据以及脑成像数据。这项研究将对癌症研究、神经科学和社会科学产生影响。大量高通量测量正在推动统计学实践的一个新分支——大规模推断。本研究项目旨在利用各种类型的稀疏性（例如，信号稀疏性，图形稀疏性，特征值稀疏性和主要特征向量稀疏性）来解决(a)网络数据收集和预处理，(b)不同类型网络的统计建模，(c)计算上可行的精确矩阵估计方法，(d)癌症分类和聚类，以及(e)稀疏主成分分析和后选择随机矩阵理论。这项研究将为社会网络、基因组学和遗传学、脑成像等应用领域的数据分析带来新的数据集和新的方法和理论。

In many application areas, high-throughput devices enable one to gather thousands and sometimes millions of measurements in very short periods of time. This research project addresses statistical problems that arise from Big Data areas such as brain imaging, genomics and genetics, and social networks. The research contains several components: (a) collect and clean large-scale data sets for social networks; (b) develop new models, methods, and theory for analyzing large social networks; and (c) develop new methods and theory for analyzing genomic and genetic data and brain imaging data. The research will have impact in cancer research, neuroscience, and social sciences. The flood of high-throughput measurements is driving a new branch of statistical practice called Large-Scale Inference. This research project aims to exploit various types of sparsity (for example, signal sparsity, graphical sparsity, sparsity in eigenvalues and leading eigenvectors) to address (a) network data collection and preprocessing, (b) statistical modeling for different types of networks, (c) computationally feasible approaches to precision matrix estimation, (d) cancer classification and clustering, and (e) sparse principal component analysis and post-selection random matrix theory. The research will lead to new data sets and new methods and theory in analyzing data in application areas such as social networks, genomics and genetics, and brain imaging.