  This paper studies the fundamental problem of learning deep generative models
that consist of multiple layers of latent variables organized in top-down
architectures. Such models have high expressivity and allow for learning
hierarchical representations. Learning such a generative model requires
inferring the latent variables for each training example based on the posterior
distribution of these latent variables. The inference typically requires Markov
chain Monte Caro (MCMC) that can be time consuming. In this paper, we propose
to use noise initialized non-persistent short run MCMC, such as finite step
Langevin dynamics initialized from the prior distribution of the latent
variables, as an approximate inference engine, where the step size of the
Langevin dynamics is variationally optimized by minimizing the Kullback-Leibler
divergence between the distribution produced by the short run MCMC and the
posterior distribution. Our experiments show that the proposed method
outperforms variational auto-encoder (VAE) in terms of reconstruction error and
synthesis quality. The advantage of the proposed method is that it is simple
and automatic without the need to design an inference model.
