Variational bayesian inference with stochastic search

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 max-imizing a lower bound on the marginal likeli-hood. This requires the ability to integrate a sum of terms in the log joint likelihood using this factorized distribution. Often not all in-tegrals 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 optimiza-tion 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 im-portant role. We demonstrate the approach on two non-conjugate models: logistic regres-sion and an approximation to the HDP. 1