Reviews: Variational Bayesian Monte Carlo

Summary: The paper considers variational inference in the case where likelihood functions themselves are expensive to evaluate. It suggests approximating the ELBO using probabilistic numerics. A Gaussian process prior is placed on the log joint of the model. A novel acquisition function is proposed along with an approximation of the ELBO for a variational mixture distribution based on the GP posterior and simple Monte Carlo for the mixture entropy. Empirical comparison is performed against a variety of relevant baselines.