  Region-based free energy was originally proposed for generalized belief
propagation (GBP) to improve loopy belief propagation (loopy BP). In this
paper, we propose a neural network based energy model for inference in general
Markov random fields (MRFs), which directly minimizes the region-based free
energy defined on region graphs. We term our model Region-based Energy Neural
Network (RENN). Unlike message-passing algorithms, RENN avoids iterative
message propagation and is faster. Also different from recent deep neural
network based models, inference by RENN does not require sampling, and RENN
works on general MRFs. RENN can also be employed for MRF learning. Our
experiments on marginal distribution estimation, partition function estimation,
and learning of MRFs show that RENN outperforms the mean field method, loopy
BP, GBP, and the state-of-the-art neural network based model.
