Layer reconstruction and missing link prediction of multilayer network with Maximum A Posteriori estimation

A multilayer network is composed of multiple layers, where different layers have the same set of vertices but represent different types of interactions. Nevertheless, some layers are interdependent or structurally similar in the multilayer network. In this paper, we present a maximum a posteriori estimation based model to reconstruct a specific layer in the multilayer network. The SimHash algorithm is used to compute the similarities between various layers. And the layers with similar structures are used to determine the parameters of the conjugate prior. With this model, we can also predict missing links and direct experiments for finding potential links. We test the method through two real multilayer networks, and the results show that the maximum a posteriori estimation is promising in reconstructing the layer of interest even with a large number of missing links.