Variational Bayesian Inference with Stochastic Search
This addresses a bottleneck in approximate Bayesian inference for researchers and practitioners working with complex models, though it is incremental as it builds on existing variational methods.
The paper tackles the problem of performing variational Bayesian inference in non-conjugate models where integrals are not in closed form, by introducing a stochastic optimization algorithm with control variates to directly optimize the variational lower bound, resulting in demonstrated applicability on logistic regression and an HDP approximation.
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.