Graphon-Level Bayesian Predictive Synthesis for Random Network

Abstract

Analysts often fit several models to the same network. Each estimates a graphon, the function giving the probability of a link between two nodes. Reporting one predictive graphon means weighting these estimates, and the weights can be constrained in several ways. We determine which constraint is correct and when the combination improves on the best single model. We introduce Bayesian predictive synthesis at the graphon level. The models enter as agents, a prior is placed on the weights combining their link probabilities, and the posterior returns one predictive graphon with credible intervals. We study this rule when the network is a union of overlapping mechanisms, so a pair is linked if at least one mechanism links it. Weights forced to sum to one cannot reproduce a union. Free and nonnegative weights do far better and do equally well. A noisy-OR rule matches the union exactly. From one observed graph we give an exact variance formula for the fitted weights, and the usual credible intervals are too narrow. On polblogs, email-Eu-core, Cora, ca-GrQc, wiki-Vote and soc-Epinions1, combining adds under one percent once a flaw in the usual benchmark is corrected, and a larger single model often wins. On the Amazon and YouTube multiplex networks, where the layers are recorded separately, it beats every competitor we tuned, including spectral estimation, blockmodels, random forests and node2vec.