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We propose to learn deep undirected graphical models (i.e., MRFs) with anon-ELBO objective for which we can calculate exact gradients. In particular,we optimize a saddle-point objective deriving from the Bethe free energyapproximation to the partition function. Unlike much recent work in approximateinference, the derived objective requires no sampling, and can be efficientlycomputed even for very expressive MRFs. We furthermore amortize thisoptimization with trained inference networks. Experimentally, we find that theproposed approach compares favorably with loopy belief propagation, but isfaster, and it allows for attaining better held out log likelihood than otherrecent approximate inference schemes.

Amortized Bethe Free Energy Minimization for Learning MRFs