  Many methods for machine learning rely on approximate inference from
intractable probability distributions. Variational inference approximates such
distributions by tractable models that can be subsequently used for approximate
inference. Learning sufficiently accurate approximations requires a rich model
family and careful exploration of the relevant modes of the target
distribution. We propose a method for learning accurate GMM approximations of
intractable probability distributions based on insights from policy search by
using information-geometric trust regions for principled exploration. For
efficient improvement of the GMM approximation, we derive a lower bound on the
corresponding optimization objective enabling us to update the components
independently. Our use of the lower bound ensures convergence to a stationary
point of the original objective. The number of components is adapted online by
adding new components in promising regions and by deleting components with
negligible weight. We demonstrate on several domains that we can learn
approximations of complex, multimodal distributions with a quality that is
unmet by previous variational inference methods, and that the GMM approximation
can be used for drawing samples that are on par with samples created by
state-of-the-art MCMC samplers while requiring up to three orders of magnitude
less computational resources.
