  We develop an optimization algorithm suitable for Bayesian learning in
complex models. Our approach relies on natural gradient updates within a
general black-box framework for efficient training with limited model-specific
derivations. It applies within the class of exponential-family variational
posterior distributions, for which we extensively discuss the Gaussian case for
which the updates have a rather simple form. Our Quasi Black-box Variational
Inference (QBVI) framework is readily applicable to a wide class of Bayesian
inference problems and is of simple implementation as the updates of the
variational posterior do not involve gradients with respect to the model
parameters, nor the prescription of the Fisher information matrix. We develop
QBVI under different hypotheses for the posterior covariance matrix, discuss
details about its robust and feasible implementation, and provide a number of
real-world applications to demonstrate its effectiveness.
