Our paper deals with a collection of networks on a common set of nodes, where some of the networks are associated with responses. Assuming that the networks correspond to points on a one-dimensional manifold in a higher dimensional ambient space, we propose an algorithm to consistently predict the response at an unlabeled network. Our model involves a specific multiple random network model, namely the common subspace independent edge model, where the networks share a common invariant subspace, and the heterogeneity amongst the networks is captured by a set of low dimensional matrices. Our algorithm estimates these low dimensional matrices that capture the heterogeneity of the networks, learns the underlying manifold by isomap, and consistently predicts the response at an unlabeled network. We provide theoretical justifications for the use of our algorithm, validated by numerical simulations. Finally, we demonstrate the use of our algorithm on larval Drosophila connectome data.

翻译：本文研究共享同一节点集合的多层网络集合，其中部分网络关联有响应变量。在假定这些网络对应高维空间中的一维流形上点的条件下，我们提出一种算法以实现对未标记网络响应的一致预测。模型采用特定的多重随机网络模型——公共子空间独立边模型，其中所有网络共享一个公共不变子空间，网络间的异质性则由一组低维矩阵刻画。所提算法通过估计表征网络异质性的低维矩阵，利用等距映射（Isomap）学习潜在流形结构，从而对未标记网络的响应进行一致预测。我们为算法应用提供了理论依据，并通过数值模拟验证其有效性。最后，我们在果蝇幼虫连接组数据上展示了算法的实际应用。