Auto-Encoding Variational Bayes

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 is two-fold. First, we show that a reparameterization of the variational lower bound with an independent noise variable yields a lower bound estimator that can be jointly optimized w.r.t. variational and generative parameters using standard gradient-based stochastic optimization methods. Second, we show that posterior inference can be made especially efficient by optimizing a probabilistic encoder (also called a recognition model) to approximate the intractable posterior, using the proposed estimator. Theoretical advantages are reflected in experimental results.