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Approximate Bayesian Computation (ABC) methods are used to approximateposterior distributions in models with unknown or computationally intractablelikelihoods. Both the accuracy and computational efficiency of ABC depend onthe choice of summary statistic, but outside of special cases where the optimalsummary statistics are known, it is unclear which guiding principles can beused to construct effective summary statistics. In this paper we explore thepossibility of automating the process of constructing summary statistics bytraining deep neural networks to predict the parameters from artificiallygenerated data: the resulting summary statistics are approximately posteriormeans of the parameters. With minimal model-specific tuning, our methodconstructs summary statistics for the Ising model and the moving-average model,which match or exceed theoretically-motivated summary statistics in terms ofthe accuracies of the resulting posteriors.

Learning Summary Statistic for Approximate Bayesian Computation via Deep Neural Network