  Gaussian distributions are widely used in Bayesian variational inference to
approximate intractable posterior densities, but the ability to accommodate
skewness can improve approximation accuracy significantly, when data or prior
information is scarce. We study the properties of a subclass of closed skew
normals constructed using affine transformation of independent standardized
univariate skew normals as the variational density, and illustrate how it
provides increased flexibility and accuracy in approximating the joint
posterior in various applications, by overcoming limitations in existing skew
normal variational approximations. The evidence lower bound is optimized using
stochastic gradient ascent, where analytic natural gradient updates are
derived. We also demonstrate how problems in maximum likelihood estimation of
skew normal parameters occur similarly in stochastic variational inference, and
can be resolved using the centered parametrization. Supplemental materials are
available online.
