Simplifying Generalized Belief Propagation on Redundant Region Graphs

摘要: The cluster variation method has been developed into a general theoretical framework for treating short-range correlations in many-body systems after it was first proposed by Kikuchi 1951. On the numerical side, message-passing approach called generalized belief propagation (GBP) Yedidia, Freeman and Weiss about decade ago as way of computing minimal value variational free energy marginal distributions clusters variables. However GBP equations are often redundant, is quite non-trivial task to make iteration converges fixed point. These drawbacks hinder application finite-dimensional frustrated disordered systems. In this work we report an alternative simple derivation starting from partition function expression. Based on propose natural systematic removing redundance equations. We apply simplified (SGBP) two-dimensional three-dimensional ferromagnetic Ising model Edwards-Anderson spin glass model. results confirm that SGBP able achieve satisfactory performance these also suggest subset can be neglected process without affecting final results.