1 / 12

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)

gyda
Télécharger la présentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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]

More Related