  We propose a black-box algorithm called {\it Adversarial Variational
Inference and Learning} (AdVIL) to perform inference and learning on a general
Markov random field (MRF). AdVIL employs two variational distributions to
approximately infer the latent variables and estimate the partition function of
an MRF, respectively. The two variational distributions provide an estimate of
the negative log-likelihood of the MRF as a minimax optimization problem, which
is solved by stochastic gradient descent. AdVIL is proven convergent under
certain conditions. On one hand, compared with contrastive divergence, AdVIL
requires a minimal assumption about the model structure and can deal with a
broader family of MRFs. On the other hand, compared with existing black-box
methods, AdVIL provides a tighter estimate of the log partition function and
achieves much better empirical results.
