  Approximate Bayesian Computation (ABC) methods are used to approximate
posterior distributions in models with unknown or computationally intractable
likelihoods. Both the accuracy and computational efficiency of ABC depend on
the choice of summary statistic, but outside of special cases where the optimal
summary statistics are known, it is unclear which guiding principles can be
used to construct effective summary statistics. In this paper we explore the
possibility of automating the process of constructing summary statistics by
training deep neural networks to predict the parameters from artificially
generated data: the resulting summary statistics are approximately posterior
means of the parameters. With minimal model-specific tuning, our method
constructs summary statistics for the Ising model and the moving-average model,
which match or exceed theoretically-motivated summary statistics in terms of
the accuracies of the resulting posteriors.
