A mean-field approximation based BP algorithm for solving the stochastic block model

Abstract

As a mainstream algorithm for inferring probabilistic graphical models, belief propagation (BP) algorithm is one of the most important methods to solve the joint probability distribution in the stochastic block model. However, existing methods either lead to low accuracy in dealing with the core-periphery structure problem, or the theoretical derivation is difficult to understand due to a large number of approximation, or both exist. Of course, the reason for low accuracy comes from too many approximations. The main reason for many approximations and complex theoretical derivation is that the joint probability distribution in the inference process of the stochastic block model is not directly solved by the BP algorithm, that is, the graph (network) being processed is not consistent with the graph considered in the probabilistic graph model. Therefore, in this paper, a mean-field approximation is developed to modify the joint probability distribution to make the BP algorithm match perfectly, which makes the theoretical derivation easy to understand. Finally, the effectiveness of the proposed method is validated by the experimental results.