Likelihood-free inference (LFI) is techniques for inference in implicit statistical models. A longstanding question in LFI has been how to design or learn good summary statistics of data, but this might now seem unnecessary due to the advent of recent end-to-end (i.e. neural network-based) LFI methods. In this work, we rethink this question with a novel method for learning summary statistics. We show that learning sufficient statistics may be easier than direct posterior inference, as the former…