Sequential Minimization of the Bethe Free Energy of Ising Spin Systems

DOI 機関リポジトリ HANDLE 被引用文献1件 参考文献14件
  • TONOSAKI Yukinori
    Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology
  • KABASHIMA Yoshiyuki
    Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology

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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.

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