Efficient analysis of latent spaces in heterogeneous networks

Abstract

In various scientific endeavors, collections of multiple networks over the same set of vertices have become increasingly prevalent. Aggregating multiple networks has proven to be valuable in unveiling intrinsic structures in multi-modal or dynamic connectivities. Nevertheless, recent studies have revealed that multiple networks can exhibit significant heterogeneity and contain both shared and individual structures simultaneously.

This presentation will investigate efficient estimation of latent structures in heterogeneous networks. In particular, this talk considers the framework of latent space models where each vertex has an associated latent embedding. A collection of networks is modeled with a shared latent embedding structure along with distinct individual embedding structures. We develop a procedure that learns both the shared and individual embedding spaces from the data. Efficient estimation is achieved by utilizing parametric efficient influence functions for the latent space parameters. We derive oracle error rates for estimating both the shared and individual latent space parameters simultaneously. The method and theory encompass a wide range of types of edge weights under general exponential family distributions.