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Kazuyuki Tanaka Graduate School of Information Sciences Tohoku University, Sendai 980-8579, Japan

Cluster Variation Method for Correlation Function of Probabilistic Model with Loopy Graphical Structure. Kazuyuki Tanaka Graduate School of Information Sciences Tohoku University, Sendai 980-8579, Japan kazu@statp.is.tohoku.ac.jp. Introduction. Cluster Variation Method (CVM)

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Kazuyuki Tanaka Graduate School of Information Sciences Tohoku University, Sendai 980-8579, Japan

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  1. Cluster Variation Methodfor Correlation Function of Probabilistic Modelwith Loopy Graphical Structure Kazuyuki Tanaka Graduate School of Information Sciences Tohoku University, Sendai 980-8579, Japan kazu@statp.is.tohoku.ac.jp

  2. Introduction • Cluster Variation Method (CVM) • Stat. Phys. [R. Kikuchi 1951] • NIPS [J. S. Yedidia et al, 2000], [H. J. Kappen et al, 2001] • Approximate marginal probability in probabilistic model + • Linear Response Theory (LRT) • MFA + LRT: H. J. Kappen et al 1998], [T. Tanaka 1998] • Correlation between any pair of nodes General CVM Approximate Formula of Correlation

  3. Linear Response Theory

  4. Final Result

  5. Basic Cluster and Subcluster • Example

  6. Probabilistic Model • Joint Probability Distribution Example

  7. Cluster Variation Method • Minimization of Free Energy

  8. Present Probabilistic Model Marginal Distribution in CVM • Probabilistic Model with External Field

  9. Linear Response in CVM

  10. Correlation Function in CVM

  11. Cluster Variation Method Numerical Experiments Exact

  12. Cluster Variation Method + Linear Response Theory • → General CVM Approximate Formula for Correlation Conclusions Extension of [H. J. Kappen et al 1998] and [T. Tanaka 1998] • Other Related Previous Work • CVM + LRT • → General CVM Approximate Formula • for Fourier Transform of Correlation • of Probabilistic Model on Regular Lattice. • [K. Tanaka, T. Horiguchi and T. Morita 1991]

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