  How can we perform efficient inference and learning in directed probabilistic
models, in the presence of continuous latent variables with intractable
posterior distributions, and large datasets? We introduce a stochastic
variational inference and learning algorithm that scales to large datasets and,
under some mild differentiability conditions, even works in the intractable
case. Our contributions are two-fold. First, we show that a reparameterization
of the variational lower bound yields a lower bound estimator that can be
straightforwardly optimized using standard stochastic gradient methods. Second,
we show that for i.i.d. datasets with continuous latent variables per
datapoint, posterior inference can be made especially efficient by fitting an
approximate inference model (also called a recognition model) to the
intractable posterior using the proposed lower bound estimator. Theoretical
advantages are reflected in experimental results.
