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2005 Fiscal Year Final Research Report Summary

Statistical mechanics of relaxation process for Bayesian inference and its application

Research Project

Project/Area Number 14084212
Research Category

Grant-in-Aid for Scientific Research on Priority Areas

Allocation TypeSingle-year Grants
Review Section Science and Engineering
Research InstitutionUniversity of Tokyo (2004-2005)
The Institute of Physical and Chemical Research (2002-2003)

Principal Investigator

OKADA Masato  University of Tokyo, Graduate School of Frontier Sciences, Professor, 大学院新領域創成科学研究科, 教授 (90233345)

Project Period (FY) 2002 – 2005
KeywordsBayesian inference / CDMA / Image reconstruction / Error Correcting code / Principal Component Analysis / Quantum annealing / Rate distortion / Relaxation process
Research Abstract

We investigated dynamics for CDMA multiuser detection. We applied the statistical neurodynamics, which is based on Gaussian approximation for input distribution, to a detection dynamics of a parallel interference canceller (PIC), and proposed a new detection algorithm based on this theoretical analysis. Recently, we have succeeded in obtaining an exact solution for the PIC detection dynamics without the Gaussian approximation using generating functional analysis (GFA). We applied a dynamical replica theory (DRT) to the CDMA detection dynamics. We also applied these theories to the image, restoration and the error-correcting code.
We proposed a numerical approach for a class of non-mean field models and finite-size models with sufficient accuracy, in which principal component analysis (PCA) is employed to analyze configurations sampled through Monte Carlo simulations. We showed that the PCA approach will be effective even with general non-MF finite-size models using examples of two-and three-body mean-field Sourlas codes.
The quantum annealing method exploits quantum fluctuations to search the ground state of classical disordered Hamiltonian, which corresponds to maximum a posteriori probability estimation. If the quantum fluctuation is reduced sufficiently slowly and linearly by the time, the residual energy after the quantum annealing falls as the inverse square of the annealing time. We show this feature of the residual energy by numerical calculations for small-sized systems and derive it on the basis of the quantum adiabatic theorem.
Additionally, we proposed a new framework for the lossy date compression using a sparsely connected random network, which was originally used on the error-correcting code.

  • Research Products

    (20 results)

All 2005 2004 2003 Other

All Journal Article (20 results)

  • [Journal Article] Generating functional analysis of CDMA detection dynamics.2005

    • Author(s)
      Mimura, Okada
    • Journal Title

      Journal of Physics A : Mathematical and General 38・46

      Pages: 9917-9929

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Approximate belief propagation, density evolution and statistical neurodynamics for CDMA multiuser detection.2005

    • Author(s)
      Tanaka, Okada
    • Journal Title

      IEEE Transaction on information theory 51

      Pages: 700-706

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Residual energies after slow quantum annealing.2005

    • Author(s)
      Suzuki, Okada
    • Journal Title

      Journal of the Physical Society of Japan 74

      Pages: 1649-1652

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Ensemble learning of linear Perceptrons : on-line learning theory.2005

    • Author(s)
      Hara, Okada
    • Journal Title

      Journal of the Physical Society of Japan Vol.74

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Analysis of ensemble learning using simple perceptrons based on online learning theory.2005

    • Author(s)
      Miyoshi, Hara, Okada
    • Journal Title

      Physical Review E Vol. 71

      Pages: 036116

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Generating functional analysis of CDMA detection Dynamics2005

    • Author(s)
      Mimura, Okada
    • Journal Title

      Journal of Physics A : Mathematical and General Vol. 38, No.46

      Pages: 9917-9929

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Approximate belief propagation, density evolution,and statistical neurodynamics for CDMA multiuser detection.2005

    • Author(s)
      Tanaka, Okada
    • Journal Title

      IEEE Transaction on information theory. Vol.51

      Pages: 700-706

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Residual energies after slow quantum annealing.2005

    • Author(s)
      Suzuki, Okada
    • Journal Title

      Journal of the Physical Society of Japan Vol.74

      Pages: 1649-1653

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Evaluation of the adaptive natural gradient descent method for soft committee machines.2004

    • Author(s)
      Inoue, Park, Okada
    • Journal Title

      Physical Review E Vol.69

      Pages: 56120-1-14

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] The path-integral analysis of an associative memory model storing an infinite number of finite limit cycles.2004

    • Author(s)
      Mimura, Kawamura, Okada
    • Journal Title

      Journal of Physics A : Mathematical and General. Vol. 37

      Pages: 6437-6454

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Accuracy of the Bethe approximation for hyperparameter estimation in probabilistic image processing.2004

    • Author(s)
      Tanaka, Shouno, Okada, Titterington.
    • Journal Title

      Journal of Physics A Vol. 37

      Pages: 8675-8696

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] One-step RSB scheme for the rate distortion functions.2003

    • Author(s)
      Murayama, Okada
    • Journal Title

      Journal of Physics A : Mathematical and General 36

      Pages: 11123-11130

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Low-dimensional chaos induced by frustration in a non-monotonic system2003

    • Author(s)
      Masaki, Tokunaga, Okada
    • Journal Title

      Europhysics Letters Vol. 62

      Pages: 657-663

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Dynamical properties of Markov Chain Monte Carlo method for image restoration.2003

    • Author(s)
      Ozeki, Okada
    • Journal Title

      Journal of Physics A : Mathematical and General. Vol. 36

      Pages: 11011-11021

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] One-step RSB scheme for the rate distortion functions.2003

    • Author(s)
      Murayama, Okada
    • Journal Title

      Journal of Physics A : Mathematical and General Vol. 36

      Pages: 11123-11130

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On-line learning dynamics of multilayer perceptrons with unidentifiable parameters.2003

    • Author(s)
      Park, Inoue, Okada
    • Journal Title

      Journal of Physics A : Mathematical and General Vol. 36

      Pages: 11753-11764

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Dynamical replica theoretic analysis of CDMA detection dynamics

    • Author(s)
      Hatchett, Okada
    • Journal Title

      Journal of Physics A : Mathematical and General (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] An analysis method combining Monte Carlo simulation and principal component analysis-application to Sourlas code

    • Author(s)
      Inoue, Hukushima, Okada
    • Journal Title

      Journal of the Physical Society of Japan (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Dynamical replica theoretic analysis of CDMA detection dynamics.

    • Author(s)
      Hatchett, Okada
    • Journal Title

      Journal of Physics A : Mathematical and General (in press)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] An analysis method combining Monte Carlo simulation and principal component analysis-application to Sourlas code

    • Author(s)
      Inoue, Hukushima, Okada
    • Journal Title

      Journal of the Physical Society of Japan (in press)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2008-05-27  

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