Loop Calculus in Statistical Physics and Information Science
  Considering a discrete and finite statistical model of a general position we introduce an exact expression for the partition function in terms of a finite series. The leading term in the series is the Bethe-Peierls (Belief Propagation)-BP contribution, the rest are expressed as loop-contributions on the factor graph and calculated directly using the BP solution. The series unveils a small parameter that often makes the BP approximation so successful. Applications of the loop calculus in statistical physics and information science are discussed. 
Michael Chertkov and Vladimir Y. Chernyak