To Relieve Your Headache of Training an MRF, Take AdVIL
This addresses the challenge of training MRFs for researchers and practitioners, offering a more flexible and effective method, though it appears incremental as it builds on existing variational and black-box approaches.
The paper tackles the problem of training Markov random fields (MRFs) by proposing AdVIL, a black-box algorithm that uses two variational distributions for inference and partition function estimation, forming a minimax optimization solved with stochastic gradient descent. It shows AdVIL requires minimal structural assumptions, handles a broader family of MRFs than contrastive divergence, and provides tighter partition function estimates with better empirical results compared to existing black-box methods.
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.