  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.
