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Paper
Auto-Encoding Variational Bayes
Authors
TL;DR
The paper addresses scalable, efficient inference in directed probabilistic models with continuous latent variables and intractable posteriors by introducing the Stochastic Gradient Variational Bayes (SGVB) estimator, enabled by a reparameterization of the variational bound. It then specializes to the Auto-Encoding VB (AEVB) framework, which learns a recognition model q_phi(z|x) to perform fast approximate posterior inference and learning, yielding the Variational Auto-Encoder when neural nets are used for encoders/decoders. The approach provides two estimator variants and demonstrates strong empirical results on MNIST and Frey Face, including favorable lower bounds and competitive marginal likelihood estimates, with scalable minibatch optimization. Overall, SGVB/AEVB offer a general, efficient pathway to learning and inference for a broad class of continuous latent-variable models, with potential applications across representation learning and generative modeling.
Abstract
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.