  We present Sequential Neural Variational Inference (SNVI), an approach to
perform Bayesian inference in models with intractable likelihoods. SNVI
combines likelihood-estimation (or likelihood-ratio-estimation) with
variational inference to achieve a scalable simulation-based inference
approach. SNVI maintains the flexibility of likelihood(-ratio) estimation to
allow arbitrary proposals for simulations, while simultaneously providing a
functional estimate of the posterior distribution without requiring MCMC
sampling. We present several variants of SNVI and demonstrate that they are
substantially more computationally efficient than previous algorithms, without
loss of accuracy on benchmark tasks. We apply SNVI to a neuroscience model of
the pyloric network in the crab and demonstrate that it can infer the posterior
distribution with one order of magnitude fewer simulations than previously
reported. SNVI vastly reduces the computational cost of simulation-based
inference while maintaining accuracy and flexibility, making it possible to
tackle problems that were previously inaccessible.
