Automatic Variational ABC

Approximate Bayesian Computation (ABC) is a framework for performing
likelihood-free posterior inference for simulation models. Stochastic Variational
inference (SVI) is an appealing alternative to the inefficient sampling approaches
commonly used in ABC. However, SVI is highly sensitive to the variance of
the gradient estimators, and this problem is exacerbated by approximating the
likelihood. We draw upon recent advances in variance reduction for SVI [6][13]
and likelihood-free inference using deterministic simulations [12] to produce low
variance gradient estimators of the variational lower-bound. By then exploiting
automatic differentiation libraries [8] we can avoid nearly all model-specific derivations.
We demonstrate performance on three problems and compare to existing
SVI algorithms. Our results demonstrate the correctness and efficiency of our
algorithm.