Nonparametric Network Comparison

科学数据越来越多地采用网络的形式，但收集和处理图形数据的能力已经超过了我们对它们进行统计分析的能力。大多数关于网络的关键科学问题都围绕着网络之间的比较（例如，随着时间的推移或跨实验条件）。这些问题出现在神经科学、流行病学、经济学、气候学和犯罪学等不同的领域。目前，网络分析师只比较基本的描述性统计数据（例如，图中节点之间的平均距离），而忽略了全局结构和统计有效性的问题。我们将发展一个严谨的网络比较统计理论。我们的方法依赖于网络理论的最新发展，该理论显示了大图如何近似连续几何对象，因此几何比较的工具可以应用于网络。我们的项目将为网络比较开发严格的统计方法和有效的算法。第一步是连续网络模型的灵活非参数估计，我们将采用三种互补策略，使用回归平滑，非欧几里得潜空间的密度估计和树的集合。在将网络表示为连续的随机过程之后，我们将发展统计理论和方法来检测和描述这些过程之间的差异。跨学科的概念验证应用，包括公共卫生（通过在线社交网络）、金融（通过金融网络）、神经科学（通过大脑连接网络）、遗传学（通过基因调控网络）和蛋白质组学（通过蛋白质相互作用网络）等领域的应用，将展示几何方法在比较大型和不同样本数据方面的力量。

Scientific data increasingly takes the form of networks, but the ability to collect and process graph data has out-paced our ability to analyze them statistically. Most of the critical scientific questions about networks revolve around comparisons between networks (e.g., over time or across experimental conditions). Such problems arise in fields as different as neuroscience, epidemiology, economics, climatology and criminology. Currently, network analysts compare only basic descriptive statistics (e.g., the average distance between nodes in the graph), ignoring issues of global structure and statistical validity. We will develop a rigorous statistical theory of network comparisons. Our approach rests on recent develops in network theory which show how large graphs approximate continuous geometric objects, so that tools for geometric comparisons can be applied to networks. Our project will develop rigorous statistical methods and efficient algorithms for network comparisons. The first step is the flexible non-parametric estimation of continuous network models, where we will pursue three complementary strategies, using regression smoothing, density estimation in non-Euclidean latent spaces, and ensembles of trees. Having represented networks as continuous stochastic processes, we will develop statistical theory and methods for detecting and characterizing differences between such processes. Interdisciplinary proof-of-concept applications, including those in public health (through online social networks), finance (through financial networks), neuroscience (through brain connectivity networks), genetics (through gene regulatory networks), and proteinomics (through protein interaction networks), will demonstrate the power of the geometric approach in comparing large and disparate sample data.