Black Box Variational Inference with a Deterministic Objective: Faster, More Accurate, and Even More Black Box

Automatic differentiation variational inference (ADVI) offers fast and easy-to-use posterior approximation in multiple modern probabilistic programming languages. However, its stochastic optimizer lacks clear convergence criteria and requires tuning parameters. Moreover, ADVI inherits the poor posterior uncertainty estimates of mean-field variational Bayes (MFVB). We introduce "deterministic ADVI" (DADVI) to address these issues. DADVI replaces the intractable MFVB objective with a fixed Monte Carlo approximation, a technique known in the stochastic optimization literature as the "sample average approximation" (SAA). By optimizing an …

approximation bayes black box box clear convergence differentiation easy faster inference languages mean modern multiple parameters posterior programming programming languages stochastic uncertainty