Collaborative Research: Inference for Network Models with Covariates: Leveraging Local Information for Statistically and Computationally Efficient Estimation of Global Parameters

协作研究：具有协变量的网络模型的推理：利用局部信息对全局参数进行统计和计算上的高效估计

• 批准号: 1713082
• 负责人: Purnamrita Sarkar
• 金额: $ 16万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-07-01 至 2021-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1713082&HistoricalAwards=false
• 关键词: Collaborative; Research; Inference; Network; Models; Collaborative; Research; Inference; Network; Models

Large datasets, which are naturally modeled as a network or graph, arise in almost every field of human endeavor. For example, Facebook is a social network, where nodes are users, with edges corresponding to friendships. In gene networks, nodes represent genes with connections corresponding to their co-expression. In ecological networks, the nodes are animal species, with edges determined according to who eats whom. A major focus of research for network or graph data has been on identifying community membership of the nodes. However, what is often more important for scientific purposes is examining the nature and evolution of edge and membership probabilities, for instance changes in gene features of individuals as a function of some unknown factor, like a disease. The focus on using other measured features of nodes and edges could add, in decisive ways, to the information available from observed edges or interactions between nodes. These could be disease symptoms or test results, or demographic information of users in social networks. Statistical inference in such models, despite its importance, has only just begun to be studied. There are both theoretical and computational challenges, due both to the complexity of models fitted, and the size of data sets. The research will lead to the development of algorithms for fitting models and statistical measures of confidence, with potential applications to many fields. The research is focused on block models for graphs, when node or edge covariates are present. When formulated, these models are no longer block models, but models whose membership probabilities depend upon covariates and whose connection probabilities depend both on block membership and individual covariates. Fitting algorithms involve alternating between fitting block and covariate parameters. Variational (mean field) approaches which effectively lead to semi-parametric model fitting with nK membership "nuisance" parameters, with n representing the number of nodes and K the number of communities, are examined. As these approaches have been found by the PIs to be unstable for large n, the PIs have already begun to investigate the theoretical and practical aspects of divide and conquer algorithms where many subgraphs are independently fit. The PIs will study the statistical properties, both asymptotically and through simulations, and develop practicable and computationally stable methods for large, relatively sparse graphs.

大型数据集自然而然地将其建模为网络或图形，几乎在人类努力的每个领域都出现。例如，Facebook是一个社交网络，节点是用户，边缘与友谊相对应。在基因网络中，节点代表具有与其共表达相对应的连接的基因。在生态网络中，节点是动物物种，其边缘是根据谁吃的人来确定的。 网络或图形数据的主要研究重点是识别节点的社区成员资格。 但是，对于科学目的而言，通常更重要的是检查边缘和成员资格概率的性质和演变，例如个体的基因特征的变化是某些未知因素（例如疾病）的函数。 使用节点和边缘的其他测量特征的重点可以以决定性的方式将观察到的边缘或节点之间的相互作用可用的信息添加到。 这些可能是疾病症状或测试结果，或者是社交网络中用户的人口信息。 尽管有重要性，但在此类模型中的统计推断才刚刚开始研究。 由于拟合的模型的复杂性和数据集的大小，都存在理论和计算挑战。 这项研究将导致开发用于拟合模型和信心统计量度的算法，并在许多领域中使用潜在的应用。当存在节点或边缘协变量时，该研究集中在图形模型上。制定后，这些模型不再是块模型，而是其成员资格概率取决于协变量且连接概率依赖于块成员资格和单个协变量的模型。 拟合算法涉及在拟合块和协变量参数之间交替。 检查了有效导致与NK成员“滋扰”参数的半参数模型拟合的变异（平均场）方法，其中N代表节点的数量和K，k被检查。 由于PIS发现这些方法对于大N不稳定，因此PI已经开始研究鸿沟和征服算法的理论和实际方面，在这些方面和征服了许多子图。 PI将在渐近和模拟上研究统计特性，并为大型，相对稀疏的图开发可行且计算稳定的方法。