  Due to the intractable partition function, training energy-based models
(EBMs) by maximum likelihood requires Markov chain Monte Carlo (MCMC) sampling
to approximate the gradient of the Kullback-Leibler divergence between data and
model distributions. However, it is non-trivial to sample from an EBM because
of the difficulty of mixing between modes. In this paper, we propose to learn a
variational auto-encoder (VAE) to initialize the finite-step MCMC, such as
Langevin dynamics that is derived from the energy function, for efficient
amortized sampling of the EBM. With these amortized MCMC samples, the EBM can
be trained by maximum likelihood, which follows an "analysis by synthesis"
scheme; while the VAE learns from these MCMC samples via variational Bayes. We
call this joint training algorithm the variational MCMC teaching, in which the
VAE chases the EBM toward data distribution. We interpret the learning
algorithm as a dynamic alternating projection in the context of information
geometry. Our proposed models can generate samples comparable to GANs and EBMs.
Additionally, we demonstrate that our model can learn effective probabilistic
distribution toward supervised conditional learning tasks.
