Abstract

Multiple-subject network data are fast emerging in recent years, where a separate connectivity matrix is measured over a common set of nodes for each individual subject, along with subject covariates information. In this article, we propose a new generalized matrix response regression model, where the observed network is treated as a matrix-valued response and the subject covariates as predictors. The new model characterizes the population-level connectivity pattern through a low-rank intercept matrix, and the effect of subject covariates through a sparse slope tensor. We develop an efficient alternating gradient descent algorithm for parameter estimation, and establish the nonasymptotic error bound for the actual estimator from the algorithm, which quantifies the interplay between the computational and statistical errors. We further show the strong consistency for graph community recovery, as well as the edge selection consistency. We demonstrate the efficacy of our method through simulations and two brain connectivity studies. Supplementary materials for this article are available online.

摘要

近年来，多主题网络数据迅速兴起，其中在每个单独主题的一组公共节点上测量单独的连接矩阵以及主题协变量信息。在本文中，我们提出了一种新的广义矩阵响应回归模型，其中观察到的网络被视为矩阵值响应，主题协变量作为预测变量。新模型通过低秩截距矩阵来表征群体水平的连通性模式，并通过稀疏斜率张量来表征主体协变量的影响。我们开发了一种用于参数估计的有效交替梯度下降算法，并根据该算法为实际估计器建立了非渐近误差界，从而量化了计算误差和统计误差之间的相互作用。我们进一步展示了图社区恢复的强一致性以及边选择的一致性。我们通过模拟和两项大脑连接研究证明了我们方法的有效性。本文的补充材料可在线获取。