  Implicit models, which allow for the generation of samples but not for
point-wise evaluation of probabilities, are omnipresent in real-world problems
tackled by machine learning and a hot topic of current research. Some examples
include data simulators that are widely used in engineering and scientific
research, generative adversarial networks (GANs) for image synthesis, and
hot-off-the-press approximate inference techniques relying on implicit
distributions. The majority of existing approaches to learning implicit models
rely on approximating the intractable distribution or optimisation objective
for gradient-based optimisation, which is liable to produce inaccurate updates
and thus poor models. This paper alleviates the need for such approximations by
proposing the Stein gradient estimator, which directly estimates the score
function of the implicitly defined distribution. The efficacy of the proposed
estimator is empirically demonstrated by examples that include meta-learning
for approximate inference, and entropy regularised GANs that provide improved
sample diversity.
