Graph metrics as summary statistics for Approximate Bayesian Computation with application to network model parameter estimation (original) (raw)
2014, Journal of Complex Networks
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. definition but is nonetheless widely used. Recently, graph metrics have gained popularity as a means of measuring in some sense the distance between the structure of two graphs. In contrast to graph measures such as the degree distribution, graphs metrics are metrics in the strict mathematical sense such that the distance between two graphs is zero only if these graphs are isomorphic. A graph metric is vital for certain tasks in applied graph theory such as estimating optimal parameters for topology generators (relative to an observed topology), determining the evolution of a dynamic graph and clustering of many graphs into different classes.
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