  We extend recent work (Brehmer, et. al., 2018) that use neural networks as
surrogate models for likelihood-free inference. As in the previous work, we
exploit the fact that the joint likelihood ratio and joint score, conditioned
on both observed and latent variables, can often be extracted from an implicit
generative model or simulator to augment the training data for these surrogate
models. We show how this augmented training data can be used to provide a new
cross-entropy estimator, which provides improved sample efficiency compared to
previous loss functions exploiting this augmented training data.
