Probability Seminar

Limit Theorems for Joint Embeddings of Multiple Random Networks


Speaker(s): Avanti Athreya (JHU)
Graph embeddings, in which the vertices of a network are mapped to vectors in a low-dimensional Euclidean space, have gained traction as a basic tool for statistical network inference. We describe a joint---or "omnibus"---embedding in which multiple graphs on the same vertex set are jointly embedded into a single space, with a distinct representation for each graph. We prove a consistency result and a central limit theorem for this omnibus procedure. Through analysis of connectome data, we show that the omnibus embedding can yield insight into network structure at different scales.