Bayesian and Spline based Approaches for (EM based) Graphon Estimation
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The paper proposes the estimation of a graphon function for network data using principles of the EM algorithm. The approach considers both, variability with respect to ordering the nodes of a network and estimation of the unique representation of a graphon. To do so (linear) B-splines are used, which allows to easily accommodate constraints in the estimation routine so that the estimated graphon fulfills the canonical representation, meaning its univariate margin is monotonic. The graphon estimate itself allows to apply Bayesian ideas to explore both, the degree distribution and the ordering of the nodes with respect to their degree. Variability and uncertainty is taken into account using MCMC techniques. Combining both steps gives an EM based approach for graphon estimation.
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