2007 Volume 13 Issue 1 Pages 57-64
A technique for minimizing the Bethe free energy of Ising spin systems is presented. The technique is based on a property of the Bethe free energy that diagonal elements of the Hessian are generally positive. This implies that solving the extremum condition with respect to a single element with fixing others at each update yields a unique solution which can be easily found by efficient algorithms such as a bisection method and reduces the value of the Bethe free energy. The proposed method, therefore, iterates sequential minimization with respect to a single element, which probably leads to convergence to a local minimum. Practical relevance of the scheme is shown by an application to a problem of multidimensional probabilistic reasoning that arises in a modern wireless communication system.
