Amortized Bethe Free Energy Minimization for Learning MRFs
This work addresses the problem of efficient and accurate learning of complex MRFs for researchers in machine learning, offering a novel inference method that is faster and more effective than existing approaches.
The paper tackles learning deep undirected graphical models (MRFs) by optimizing a saddle-point objective derived from the Bethe free energy approximation, which avoids sampling and computes exact gradients efficiently. The result shows favorable performance compared to loopy belief propagation, with faster speed and better held-out log likelihood than other approximate inference schemes.
We propose to learn deep undirected graphical models (i.e., MRFs) with a non-ELBO objective for which we can calculate exact gradients. In particular, we optimize a saddle-point objective deriving from the Bethe free energy approximation to the partition function. Unlike much recent work in approximate inference, the derived objective requires no sampling, and can be efficiently computed even for very expressive MRFs. We furthermore amortize this optimization with trained inference networks. Experimentally, we find that the proposed approach compares favorably with loopy belief propagation, but is faster, and it allows for attaining better held out log likelihood than other recent approximate inference schemes.