Statistics Seminar

Abstract: Graph matching is the problem of aligning the vertices of two unlabeled graphs in order to maximize the shared structure across them. This talk will highlight some recent likelihood-based approaches for this problem. The first part of the talk will focus on unipartite networks, where one of the graphs is an errorfully observed copy of the other. We present necessary and sufficient conditions for consistency of the maximum likelihood estimator, and use these to study matchability in different families of random graphs. The second part will discuss the problem of graph matching between bipartite and unipartite networks. We formulate the problem via undirected graphical models, and study the connections between graph matching and graphical model estimation. The methods are illustrated in simulated data and real brain networks.