Loop Calculus in Statistical Physics and Information Science
<|reference_start|>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.<|reference_end|>
@article{chertkov2006loop,
    title={Loop Calculus in Statistical Physics and Information Science},
    author={Michael Chertkov and Vladimir Y. Chernyak},
    journal={Phys. Rev. E 73, 065102(R) (2006)},
    year={2006},
    doi={10.1103/PhysRevE.73.065102},
    number={LAUR-06-0443},
    archivePrefix={arXiv},
    eprint={cond-mat/0601487},
    primaryClass={cond-mat.stat-mech cond-mat.dis-nn cs.IT math.IT}
}