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 SV and likelihood-free inference using deterministic simulations to produce low variance gradient estimators of the variational lower-bound. By then exploiting automatic differentiation libraries 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.
@cite_2: Variational inference is a scalable technique for approximate Bayesian inference. Deriving variational inference algorithms requires tedious model-specific calculations; this makes it difficult for non-experts to use. We propose an automatic variational inference algorithm, automatic differentiation variational inference (ADVI); we implement it in Stan (code available), a probabilistic programming system. In ADVI the user provides a Bayesian model and a dataset, nothing else. We make no conjugacy assumptions and support a broad class of models. The algorithm automatically determines an appropriate variational family and optimizes the variational objective. We compare ADVI to MCMC sampling across hierarchical generalized linear models, nonconjugate matrix factorization, and a mixture model. We train the mixture model on a quarter million images. With ADVI we can use variational inference on any model we write in Stan.
@cite_2 used automatic differentiation to fully automate variational inference, which we refer to as AVI. AVI fits a Gaussian variational distribution in a transformed space, leading to a non-Gaussian approximation in the original space when transformed back. This limits the range of variational distributions. In the transformed space they make a fully-factorized mean-field assumption. AVI requires rewriting the simulator in STAN. With complex simulators, this is unrealistic and negates the main benefit: that it is automatic.