Information geometry of mean-field approximation
Related Experiment Video
Updated: Oct 13, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
1Department of Electronics and Information Engineering, Tokyo Metropolitan University, Tokyo 192-0397, Japan.
Abstract:
I present a general theory of mean-field approximation based on information geometry and applicable not only to Boltzmann machines but also to wider classes of statistical models. Using perturbation expansion of the Kullback divergence (or Plefka expansion in statistical physics), a formulation of mean-field approximation of general orders is derived. It includes in a natural way the "naive" mean-field approximation and is consistent with the Thouless-Anderson-Palmer (TAP) approach and the linear response theorem in statistical physics.
Related Concept Videos
Geometric Mean
In cases of multiplicative data, the geometric mean is used for statistical analysis. First, the product of all the elements is taken. Then, if there are n elements in the...
The Mean Value Theorem
Gauss's Law
Linear Approximations
Estimation of the Physical Quantities
Accuracy, limits, and approximation
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...
