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应用催生了脑连接组学的新领域，该领域研究大脑不同区域之间的连接模式。该项目汇集了研究者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，并将其主要应用于从精神疾病患者和健康患者的功能磁共振成像推断出的大脑连接网络，目的是使用可靠的统计推断来发现他们的大脑有何不同。这些方法利用底层公共结构跨网络共享信息，并识别与疾病状态和其他诊断评估相关的结构网络特征。从脑成像中收集的原始fMRI数据通常被转换为网络表示，然后对其进行分析，以找到正常人脑活动的模式以及与各种精神障碍相关的异常。因此，数据本质上是网络的一个样本，每个主题一个。然而，目前在脑连接组学中使用的网络分析工具通常局限于简单的网络全局摘要；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了，这种分析分别观察每个连接。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，但是几乎没有任何统计方法能够以一种既尊重又利用网络结构的方式处理网络样本。该项目将通过开发新的网络样本统计方法，并将其应用于脑连接组学问题，弥合这一差距。我们的第一个目标是开发从网络的噪声样本中估计“总体均值”（特别是底层社区）的方法。该项目提出了一种em型算法，该算法通过利用底层公共结构来优于朴素平均。第二个目标是为网络设计新的精确分类器，它可以通过基于边缘之间的空间和网络距离的惩罚来识别可解释的预测特征，例如子网。第三个目标是开发受典型关联启发的网络相似性的新测量方法，该方法可用于网络分类和聚类，后者对于发现表现为精神疾病不同亚型的大脑连接障碍亚型尤其重要。该项目还将研究网络结构变异性的测量方法和预测疾病状态的方法，以及更复杂的多变量诊断评估。这些方法的发展将对神经科学和心理健康的研究产生直接影响，该项目将通过与两个脑成像实验室密切合作，并在统计学和连接组学社区传播结果，确保方法的相关性和可行性。该项目还将有助于培养网络分析和脑连接组学方面的研究生。

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.