  This paper studies the fundamental learning problem of the energy-based model
(EBM). Learning the EBM can be achieved using the maximum likelihood estimation
(MLE), which typically involves the Markov Chain Monte Carlo (MCMC) sampling,
such as the Langevin dynamics. However, the noise-initialized Langevin dynamics
can be challenging in practice and hard to mix. This motivates the exploration
of joint training with the generator model where the generator model serves as
a complementary model to bypass MCMC sampling. However, such a method can be
less accurate than the MCMC and result in biased EBM learning. While the
generator can also serve as an initializer model for better MCMC sampling, its
learning can be biased since it only matches the EBM and has no access to
empirical training examples. Such biased generator learning may limit the
potential of learning the EBM. To address this issue, we present a joint
learning framework that interweaves the maximum likelihood learning algorithm
for both the EBM and the complementary generator model. In particular, the
generator model is learned by MLE to match both the EBM and the empirical data
distribution, making it a more informative initializer for MCMC sampling of
EBM. Learning generator with observed examples typically requires inference of
the generator posterior. To ensure accurate and efficient inference, we adopt
the MCMC posterior sampling and introduce a complementary inference model to
initialize such latent MCMC sampling. We show that three separate models can be
seamlessly integrated into our joint framework through two (dual-) MCMC
teaching, enabling effective and efficient EBM learning.
