[1312.6114] Auto-Encoding Variational Bayes
datasets and continuous latent variables per datapoint we introduce an efficient algorithm for efficient inference and learning, Auto-Encoding VB (AEVB), that learns an approximate inference model using the SGVB estimator

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 is 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.

‹Figure 1: The type of directed graphical model under consideration. Solid lines denote the generative model pθ(z)pθ(x|z), dashed lines denote the variational approximation qφ(z|x) to the intractable posterior pθ(z|x). The variational parameters φ are learned jointly with the generative model parameters θ. (Method)

Figure 4: Learned Frey Face manifold Figure 5: Learned MNIST manifold Figure 6: Visualisations of learned data manifold for generative models with two-dimensional latent space, learned with AEVB. Since the prior of the latent space is Gaussian, linearly spaced coordinates on the unit square were transformed through the inverse CDF of the Gaussian to produce values of the latent variables z. For each of these values z, we plotted the corresponding generative pθ(x|z) with the learned parameters θ. (Future work)Figure 7: 2-D latent space Figure 8: 5-D latent space Figure 9: 10-D latent space Figure 10: 20-D latent space Figure 11: Random samples from learned generative models of MNIST for different dimensionalities of latent space. (Future work)