Generalized Connectivity Matrix Response Regression with Applications in Brain Connectivity Studies
Generalized Connectivity Matrix Response Regression with Applications in Brain Connectivity Studies
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DOI：
10.1080/10618600.2022.2074434
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发表时间：
2018-10
影响因子：
2.4
通讯作者：
Jingfei Zhang;W. Sun;Lexin Li
中科院分区：
文献类型：
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作者：
Jingfei Zhang;W. Sun;Lexin Li
摘要近年来，多主题网络数据迅速涌现，其中针对每个单独主题在公共节点集合上测量单独的连接性矩阵以及主题协变量信息。在本文中，我们提出了一个新的广义矩阵响应回归模型，其中观测网络被视为矩阵值响应，被试协变量作为预测变量。新模型通过低阶截距矩阵刻画种群水平的连通性模式，通过稀疏斜率张量描述主体协变量的影响。我们提出了一种有效的交替梯度下降算法用于参数估计，并由该算法得到了实际估计的非渐近误差界，它量化了计算误差和统计误差之间的相互影响。进一步证明了图社区恢复的强一致性，以及边选择的一致性。我们通过模拟和两个大脑连通性研究证明了我们方法的有效性。这篇文章的补充材料可以在网上找到。
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.