We develop an automated variational method for approximate inference in Gaussian process (GP) models whose posteriors are often intractable. Using a mixture of Gaussians as the variational distribution, we show that (i) the variational objective and its gradients can be approximated efficiently via sampling from univariate Gaussian distributions and (ii) the gradients of the GP hyperparameters can be obtained analytically regardless of the model likelihood. We further propose two instances of the variational distribution whose covariance matrices can be parametrized linearly in the number of observations. These results allow gradient-based optimization to be done efficiently in a black-box manner. Our approach is thoroughly verified on 5 models using 6 benchmark datasets, performing as well as the exact or hard-coded implementations while running orders of magnitude faster than the alternative MCMC sampling approaches. Our method can be a valuable tool for practitioners and researchers to investigate new models with minimal effort in deriving model-specific inference algorithms.

We develop an automated variational method for approximate inference in Gaussian process (GP) models whose posteriors are often intractable. Using a mixture of Gaussians as the variational distribution, we show that (i) the variational objective and its gradients can be approximated efficiently via sampling from univariate Gaussian distributions and (ii) the gradients of the GP hyperparameters can be obtained analytically regardless of the model likelihood. We further propose two instances of the variational distribution whose covariance matrices can be parametrized linearly in the number of observations. These results allow gradient-based optimization to be done efficiently in a black-box manner. Our approach is thoroughly verified on 5 models using 6 benchmark datasets, performing as well as the exact or hard-coded implementations while running orders of magnitude faster than the alternative MCMC sampling approaches.

We present a new algorithm for approximate inference in probabilistic programs, based on a stochastic gradient for variational programs. This method is efficient without restrictions on the probabilistic program; it is particularly practical for distributions which are not analytically tractable, including highly structured distributions that arise in probabilistic programs. We show how to automatically derive mean-field probabilistic programs and optimize them, and demonstrate that our perspective improves inference efficiency over other algorithms.