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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 http://www.statp.is.tohoku.ac.jp/~kazu/index-e.html.

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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 http://www.statp.is.tohoku.ac.jp/~kazu/index-e.html University of Glasgow

  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 University of Glasgow

  3. Linear Response Theory University of Glasgow

  4. Linear Response Theory University of Glasgow

  5. Final Result University of Glasgow

  6. Basic Cluster and Subcluster • Example University of Glasgow

  7. Probabilistic Model • Joint Probability Distribution Example University of Glasgow

  8. Cluster Variation Method • Kullback-Leibler Divergence and Kikuchi Free Energy University of Glasgow

  9. Present Probabilistic Model Marginal Distribution in CVM • Probabilistic Model with External Field University of Glasgow

  10. Linear Response in CVM University of Glasgow

  11. Correlation Function in CVM University of Glasgow

  12. Cluster Variation Method Numerical Experiments Exact University of Glasgow

  13. 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] University of Glasgow

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