Multivariate Analysis for Samples of Networks

以网络形式收集的数据，通常带有加权边，在实践中变得越来越普遍，但经典的统计工具不适用于此类数据。这个项目将为几种常见的统计分析开发一个网络感知方法的统计工具箱。主要的激励应用是神经成像，它允许收集人类受试者的大脑连接网络数据。这些方法可用于识别与疾病相关的大脑连接模式，估计儿童和青少年正常的大脑发育轨迹及其偏离，研究与老年人正常和异常衰老相关的变化，并发现已知疾病的新亚型。这些方法将在与神经科学家的密切合作下进行开发和广泛测试。本项目开发用于向量值数据的通用多变量分析工具的网络模拟，如估计平均值、分类、聚类和主成分分析。总体主题是开发网络感知方法，通过在将网络崩溃为几个全局汇总度量和将它们视为边缘权重的长单个向量之间取得平衡，目标是获得不仅准确而且科学可解释的方法。一般来说，开发这种方法的技术挑战来自于需要将高级网络结构（如社区）强加到低级网络特征（如单个边权重）上。解决这些挑战将涉及现代随机矩阵理论、结构化惩罚、先进的优化技术和计算效率高的算法等复杂工具，这些工具将为每一个新的网络分析工具开发。与神经科学家和精神病学家的密切合作将确保所开发的统计工具在神经影像学社区得到彻底的测试和审查。项目结果将通过出版物、演讲和软件包在统计和神经成像领域广泛传播，并有望提高脑连接组学领域统计网络分析的当前标准。该项目还将在现代统计学的一个重要新兴领域培养研究生，并帮助他们发展先进的计算和跨学科协作技能。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Data collected in the form of networks, often with weighted edges, have become increasingly common in practice, but classical statistical tools do not apply to such data. This project will develop a statistical toolbox of network-aware methods for several common statistical analyses. The main motivating application is neuroimaging, which allows collecting brain connectivity network data from human subjects. These methods can be used to identify brain connectivity patterns associated with disorders, to estimate normal brain development trajectories and deviations from it for children and adolescents, to study changes associated with normal and abnormal aging in older subjects, and to find new subtypes of known disorders. The methods will be developed and extensively tested in close collaboration with neuroscientists.This project develops network analogues for common multivariate analysis tools for vector-valued data, such as estimating the mean, classification, clustering, and principal component analysis. The overarching theme is developing network-aware methods by striking the balance between collapsing the networks to a few global summary measures and treating them as a long single vector of edge weights, with the goal to obtain methods that are not only accurate, but also scientifically interpretable. The technical challenges in developing such methods arise, broadly speaking, from the need to impose high-level network structure, such as communities, onto low-level network features, such as individual edge weights. Addressing these challenges will involve sophisticated tools from modern random matrix theory, structured penalties, advanced optimization techniques, and computationally efficient algorithms, to be developed for each of the new network analysis tools proposed. The close collaboration with neuroscientists and psychiatrists will ensure that the statistical tools developed are thoroughly tested and vetted in the neuroimaging community. Project results will be widely disseminated through publications, presentations, and software packages, in both statistical and neuroimaging venues, and are expected to raise the current standards for statistical network analysis in the field of brain connectomics. The project will also train graduate students in an important emerging area of modern statistics and help them develop advanced computing and interdisciplinary collaboration skills.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.