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Information geometry of mean-field approximation.

T Tanaka1

  • 1Department of Electronics and Information Engineering, Tokyo Metropolitan University, Tokyo 192-0397, Japan.

Neural Computation
|August 23, 2000
PubMed
Summary
This summary is machine-generated.

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This study introduces a general theory for mean-field approximation using information geometry. This new approach applies to various statistical models, including Boltzmann machines, and offers a unified framework for understanding approximations.

Area of Science:

  • Statistical Physics
  • Information Geometry
  • Machine Learning

Background:

  • Mean-field approximation is a crucial technique in statistical physics and machine learning.
  • Existing methods like naive mean-field and Thouless-Anderson-Palmer (TAP) have limitations.
  • A unified theoretical framework is needed for broader applicability.

Purpose of the Study:

  • To develop a general theory of mean-field approximation grounded in information geometry.
  • To extend the applicability of mean-field methods beyond traditional models like Boltzmann machines.
  • To provide a unified framework consistent with existing approximation techniques.

Main Methods:

  • Utilizing information geometry as the foundational framework.
  • Employing perturbation expansion of Kullback divergence (Plefka expansion).

Related Experiment Videos

  • Deriving a general formulation for mean-field approximation of arbitrary orders.

    • Main Results:

    • A novel, general theory for mean-field approximation is presented.
    • The theory naturally incorporates the naive mean-field approximation.
    • The derived formulation is consistent with the Thouless-Anderson-Palmer (TAP) approach and linear response theory.

    Conclusions:

    • The information geometry approach provides a powerful and unified framework for mean-field approximations.
    • This general theory enhances the understanding and application of mean-field methods in diverse statistical models.
    • The findings bridge statistical physics and machine learning, offering new avenues for research.