  Mean-field variational inference is a method for approximate Bayesian
posterior inference. It approximates a full posterior distribution with a
factorized set of distributions by maximizing a lower bound on the marginal
likelihood. This requires the ability to integrate a sum of terms in the log
joint likelihood using this factorized distribution. Often not all integrals
are in closed form, which is typically handled by using a lower bound. We
present an alternative algorithm based on stochastic optimization that allows
for direct optimization of the variational lower bound. This method uses
control variates to reduce the variance of the stochastic search gradient, in
which existing lower bounds can play an important role. We demonstrate the
approach on two non-conjugate models: logistic regression and an approximation
to the HDP.
