To Relieve Your Headache of Training an MRF, Take AdVIL

TL;DR

AdVIL is a black-box algorithm that efficiently performs inference and learning on general Markov random fields using a minimax variational approach, improving accuracy and broad applicability over existing methods.

Contribution

The paper introduces AdVIL, a novel black-box variational inference algorithm for MRFs that offers tighter estimates and broader applicability than prior methods.

Findings

AdVIL provides a tighter estimate of the log partition function.

AdVIL achieves better empirical results than existing black-box methods.

AdVIL requires minimal assumptions about the MRF structure.

Abstract

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.