In increasingly many settings, data sets consist of multiple samples from a population of networks, with vertices aligned across these networks. For example, brain connectivity networks in neuroscience consist of measures of interaction between brain regions that have been aligned to a common template. We consider the setting where the observed networks have a shared expectation, but may differ in the noise structure on their edges. Our approach exploits the shared mean structure to denoise edge-level measurements of the observed networks and estimate the underlying population-level parameters. We also explore the extent to which edge-level errors influence estimation and downstream inference. We establish a finite-sample concentration inequality for the low-rank eigenvalue truncation of a random weighted adjacency matrix that may be of independent interest. The proposed approach is illustrated on synthetic networks and on data from an fMRI study of schizophrenia.

翻译：在越来越多的环境中,数据集由多个网络群的多个样本组成,这些网络的脊椎对齐。例如,神经科学中的大脑连通网络包括大脑区域之间互动的计量,这些计量已经与共同模板一致。我们考虑观测到的网络具有共同期望,但其边缘的噪音结构可能不同。我们的方法利用共同平均结构对观测到的网络进行隐蔽边缘水平的测量,并估计潜在的人口参数。我们还探索边缘水平错误影响估计和下游推断的程度。我们为低层半数值的随机加权相邻矩阵设定了一定的浓度不平等,这可能具有独立的兴趣。拟议方法在合成网络和对精神分裂症进行的一项FMRI研究的数据上作了说明。