Approximate Inference and Protein-Folding
Side-chain prediction is an important subtask in the protein-folding problem. We show that finding a minimal energy side-chain configuration is equivalent to performing inference in an undirected graphical model. The graphical model is relatively sparse yet has many cycles. We used this equivalence to assess the performance of approximate inference algorithms in a real-world setting. Specifically we compared belief propagation (BP), generalized BP (GBP) and naive mean field (MF). 
 
In cases where exact inference was possible, max-product BP always found the global minimum of the energy (except in few cases where it failed to converge), while other approximation algorithms of similar complexity did not. In the full protein data set, max-product BP always found a lower energy configuration than the other algorithms, including a widely used protein-folding software (SCWRL).