Improving Variational Auto-Encoders using Householder Flow

Variational auto-encoders (VAE) are scalable and powerful generative models. However, the choice of the variational posterior determines tractability and flexibility of the VAE. Commonly, latent variables are modeled using the normal distribution with a diagonal covariance matrix. This results in computational efficiency but typically it is not flexible enough to match the true posterior distribution. One fashion of enriching the variational posterior distribution is application of normalizing flows, i.e., a series of invertible transformations to latent variables with a simple posterior. In this paper, we follow this line of thinking and propose a volume-preserving flow that uses a series of Householder transformations. We show empirically on MNIST dataset and histopathology data that the proposed flow allows to obtain more flexible variational posterior and highly competitive results comparing to other normalizing flows. 1 Variational Auto-Encoder Let x be a vector of D observable variables, z ∈ R a vector of stochastic latent units (variables) and let p(x, z) be a parametric model of the joint distribution. Given N datapoints X = {x1, . . . ,xN} we typically aim at maximizing the marginal log-likelihood: