Graph metrics as summary statistics for Approximate Bayesian Computation with application to network model parameter estimation

In this paper, we investigate Approximate Bayes Computation as a technique for estimating the parameters of graph generators relative to an observed graph. Specifically, we investigate six spectral graph metrics with a view to evaluating their suitability as summary statistics. The overall findings are that Approximate Bayesian Computation can result in reasonable estimates of the parameter posteriors, if the rank of the metrics is sufficiently high. For some graph metrics, biases can exist in the estimated parameters though these appear, empirically, to be small. We demonstrate that combining metrics to form a new summary statistic provides more robust estimates. Given these results, the authors then create two, somewhat arbitrary, graph generators and show how the parameters for these may be estimated with ease. In addition, we show how to apply model selection to determine which generator best explains the observed graph.