Generalized Connectivity Matrix Response Regression with Applications in Brain Connectivity Studies
提出一种广义矩阵响应回归模型，将观测到的脑网络作为矩阵响应、被试协变量作为预测变量，通过低秩截距和稀疏斜率张量刻画群体连接模式与协变量效应，并开发交替梯度下降算法进行参数估计。
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 non-asymptotic 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.