  Natural-gradient methods enable fast and simple algorithms for variational
inference, but due to computational difficulties, their use is mostly limited
to \emph{minimal} exponential-family (EF) approximations. In this paper, we
extend their application to estimate \emph{structured} approximations such as
mixtures of EF distributions. Such approximations can fit complex, multimodal
posterior distributions and are generally more accurate than unimodal EF
approximations. By using a \emph{minimal conditional-EF} representation of such
approximations, we derive simple natural-gradient updates. Our empirical
results demonstrate a faster convergence of our natural-gradient method
compared to black-box gradient-based methods with reparameterization gradients.
Our work expands the scope of natural gradients for Bayesian inference and
makes them more widely applicable than before.
