Statistical Tools for Analyzing Multiple Networks

功能磁共振成像(FMRI)和其他神经成像技术的广泛使用催生了脑连接学的一个新领域，它研究大脑不同区域之间的连接模式。该项目汇集了研究人员在网络统计分析方面的专业知识，以及她与神经科学家的合作，开发了同时对多个网络进行统计分析的新方法，并将它们主要应用于从精神疾病患者和健康患者的fMRI成像中推断出的大脑连接网络，目的是使用合理的统计推断来发现他们的大脑有何不同。这些方法利用基本的公共结构在网络之间共享信息，并确定与疾病状态和其他诊断评估相关联的结构网络特征。从大脑成像收集的原始fMRI数据通常被转换为网络表示，然后进行分析，以找到正常人类大脑活动的模式以及与各种精神障碍相关的异常。因此，这些数据本质上是一个网络样本，每个对象一个。然而，目前网络分析工具在脑连接学中的使用通常局限于对网络的简单全局总结；更常见的是，在所谓的大规模单变量分析中，网络结构被完全忽略，该分析分别研究每个连接。与此同时，网络社区已经开发了大量的方法来分析单个网络的结构，例如发现社区，但几乎没有任何统计方法可以同时尊重和利用网络结构的方式处理网络样本。这个项目将通过为网络样本开发新的统计方法来弥补这一差距，并将其应用于大脑连接学中的问题。我们的第一个目标是开发从嘈杂的网络样本中估计“人口平均值”(特别是底层社区)的方法。这个项目提出了一种EM类型的算法，它通过利用底层的公共结构来超越朴素平均。第二个目标是为网络设计新的准确的分类器，它可以通过基于边之间的空间距离和网络距离的惩罚来识别可解释的预测特征，如子网络。第三个目标是开发受典型相关性启发的新的网络相似性测量方法，可用于网络分类和聚类，后者对于发现表现为不同亚类型精神障碍的大脑连通性障碍的亚类型尤其重要。该项目还将调查网络结构的可变性测量，以及不仅预测疾病状态，而且预测更复杂的多变量诊断评估的方法。这些方法的开发将对神经科学和心理健康的研究产生直接影响，该项目将与两个脑成像实验室密切合作，并在统计和连接学社区传播结果，从而确保方法的相关性和可行性。该项目还将有助于对研究生进行网络分析和大脑连接学的培训。

The widespread use of functional magnetic resonance imaging (fMRI) and other neuroimaging technologies has given rise to a new field of brain connectomics, which studies patterns of connections between different regions of the brain. This project brings together the investigator's expertise on statistical analysis of networks and her collaboration with neuroscientists to develop new methods for simultaneous statistical analysis of multiple networks and apply them primarily to brain connectivity networks inferred from fMRI imaging of mentally ill and healthy patients, with the goal of using sound statistical inference to discover how their brains differ. The methods leverage underlying common structure to share information across networks and identify structural network features associated with disease status and other diagnostic assessments. The raw fMRI data collected from brain imaging are typically converted to network representations, which are then analyzed to find patterns of normal human brain activity as well as abnormalities associated with various mental disorders. Thus the data are essentially a sample of networks, one for each subject. However, the current use of network analysis tools in brain connectomics is typically confined to simple global summaries of the network; even more commonly, the network structure is ignored altogether in what is known as massively univariate analysis, which looks at each connection separately. At the same time, the networks community has developed a wealth of methods for analyzing the structure of a single network, for example, discovering communities, but there are hardly any statistical methods that can handle samples of networks in a way that both respects and exploits network structure. This project will bridge this gap by developing new statistical methodology for samples of networks, and applying it to problems in brain connectomics. Our first goal is developing methods to estimate the "population mean" (in particular the underlying communities) from a noisy sample of networks. This project proposes an EM-type algorithm which outperforms naive averaging by exploiting the underlying common structure. The second goal is designing new accurate classifiers for networks which can identify interpretable predictive features such as subnetworks by using penalties based on both spatial and network distances between edges. The third goal is developing new measures of network similarity inspired by canonical correlations, which can be used for both network classification and clustering, the latter especially important for discovering subtypes of brain connectivity disorders which manifest themselves as different subtypes of psychiatric disorders. This project will also investigate measures of variability of network structure and methods for predicting not only disease status, but more complex multivariate diagnostic assessments. Development of these methods will have direct impact on research in neuroscience and mental health, and this project will ensure the methods relevance and feasibility by working in close collaboration with two brain imaging labs and disseminating the results both in the statistics and the connectomics communities. The project will also contribute to training graduate students in both network analysis and brain connectomics.