We develop an automated variational method for inference in models with Gaussian process (GP) priors and general likelihoods. The method supports multiple outputs and multiple latent functions and does not require detailed knowledge of the conditional likelihood, only needing its evaluation as a black-box function. Using a mixture of Gaussians as the variational distribution, we show that the evidence lower bound and its gradients can be estimated efficiently using samples from univariate Gaussian distributions. Furthermore, the method is scalable to large datasets which is achieved by using an augmented prior via the inducing-variable approach underpinning most sparse GP approximations, along with parallel computation and stochastic optimization. We evaluate our approach quantitatively and qualitatively with experiments on small datasets, medium-scale datasets and large datasets, showing its competitiveness under different likelihood models and sparsity levels. On the large-scale experiments involving prediction of airline delays and classification of handwritten digits, we show that our method is on par with the state-of-the-art hard-coded approaches for scalable GP regression and classification.
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