  To train an inference network jointly with a deep generative topic model,
making it both scalable to big corpora and fast in out-of-sample prediction, we
develop Weibull hybrid autoencoding inference (WHAI) for deep latent Dirichlet
allocation, which infers posterior samples via a hybrid of stochastic-gradient
MCMC and autoencoding variational Bayes. The generative network of WHAI has a
hierarchy of gamma distributions, while the inference network of WHAI is a
Weibull upward-downward variational autoencoder, which integrates a
deterministic-upward deep neural network, and a stochastic-downward deep
generative model based on a hierarchy of Weibull distributions. The Weibull
distribution can be used to well approximate a gamma distribution with an
analytic Kullback-Leibler divergence, and has a simple reparameterization via
the uniform noise, which help efficiently compute the gradients of the evidence
lower bound with respect to the parameters of the inference network. The
effectiveness and efficiency of WHAI are illustrated with experiments on big
corpora.
