A Mixture Model Approach for Continuous Graphon Models
Benjamin Sischka, Göran KauermannWe propose a novel method for graphon estimation which allows us to model mixtures of smooth graphon models for network data. The resulting graphon object can furthermore be seen as a blockmodel with smooth variations within the groups. In doing so also the degree heterogeneity, which is a well-known issue in common blockmodeling strategies, can be handled naturally. For the estimation, we are constructing an MCEM algorithm. The approach encompasses node allocation for both between and within groups as well as piecewise smooth estimation of the graphon function by semiparametric regression. The latter concept is achieved through the use of (linear) B-splines with non-overlapping bases. This allows accommodating clear splits in the graphon function which yields group allocations. Moreover, other constraints can be included in the estimation routine, such as symmetry in the case of undirected networks. The uncertainty inherent in the estimation is quantified by using MCMC techniques. Combining both steps gives an EM-based approach for estimating mixtures of smooth graphon models.