  We consider the fundamental problem of how to automatically construct summary
statistics for implicit generative models where the evaluation of the
likelihood function is intractable, but sampling data from the model is
possible. The idea is to frame the task of constructing sufficient statistics
as learning mutual information maximizing representations of the data with the
help of deep neural networks. The infomax learning procedure does not need to
estimate any density or density ratio. We apply our approach to both
traditional approximate Bayesian computation and recent neural likelihood
methods, boosting their performance on a range of tasks.
