Black box variational inference

Variational inference has become a widely used method to approximate posteriors in complex latent variables models. However, deriving a variational inference algorithm gen-erally requires significant model-specific anal-ysis. These efforts can hinder and deter us from quickly developing and exploring a vari-ety of models for a problem at hand. In this paper, we present a “black box ” variational inference algorithm, one that can be quickly applied to many models with little additional derivation. Our method is based on a stochas-tic optimization of the variational objective where the noisy gradient is computed from Monte Carlo samples from the variational dis-tribution. We develop a number of methods to reduce the variance of the gradient, always maintaining the criterion that we want to avoid difficult model-based derivations. We evaluate our method against the correspond-ing black box sampling based methods. We find that our method reaches better predictive likelihoods much faster than sampling meth-ods. Finally, we demonstrate that Black Box Variational Inference lets us easily explore a wide space of models by quickly constructing and evaluating several models of longitudinal healthcare data.