Omnibus Embeddings for Mutliple Graph Inference

• Activity Number: 455 - Recent Advances in Multiple Graph Inference
• Type: Invited
• Date/Time: Wednesday, August 1, 2018 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Avanti Athreya* and Keith Levin and Minh Tang and Carey E Priebe and Vince Lyzinski
• Companies: Johns Hopkins University and University of Michigan and Johns Hopkins University and Johns Hopkins University and University of Massachusetts Amherst
• Keywords: Graph embeddings; Spectral decompositions; Multiple-graph inference

Abstract

Performing statistical inference on collections of graphs is of import to many disciplines. Graph embedding, in which the vertices of a graph are mapped to vectors in a low-dimensional Euclidean space, has gained traction as a basic tool for graph analysis, and in this talk we describe an omnibus embedding in which multiple graphs on the same vertex set are jointly embedded into a single space, but with a distinct representation for each graph. We prove a limit theorem for this omnibus embedding, and we show that this simultaneous embedding into a common space allows for comparison of graphs without the need to perform pairwise alignments of graph embeddings. Experimental results demonstrate that on certain latent position graphs, the omnibus embedding performs nearly optimally for latent position estimation, but exhibits better power in multiple-graph hypothesis testing. We discuss current research and open problems on the relative merits of separate and omnibus embeddings for different inference tasks