Probabilistic inference by means of cluster variation method and linear response theory

Probabilistic inference by means of a massive probabilistic model usually has exponential-order computational complexity. For such massive probabilistic model, loopy belief propagation was proposed as a scheme to obtain the approximate inference. It is known that the generalized loopy belief propagation is constructed by using a cluster variation method. However, it is difficult to calculate the correlation in every pair of nodes which are not connected directly to each other by means of the generalized loopy belief propagation. In the present paper, we propose a general scheme for calculating an approximate correlation in every pair of nodes in a probabilistic model for probabilistic inference. The general scheme is formulated by combining a cluster variation method with a linear response theory.