A Refined Mean Field Approximation

A Theory of Mean Field Approximation

I present a theory of mean field approximation based on information geometry. This theory includes in a consistent way the naive mean field approximation, as well as the TAP approach and the linear response theorem in statistical physics, giving clear information-theoretic interpretations to them.

A Mean Field Approximation of BCPNN

In this report we study a mean field (MF) approximation of the Bayesian Confidence Propagating Neural Network (BCPNN) for which we derive the energy function. This MF approximation is compared with the original formulation of the network in a number of different tasks in order to establish the similarities and dissimilarities. We investigate the effect of different updating strategies on the st...

Mean Field Approximation for Fields of Experts

Information Geometry of Mean-Field Approximation

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" me...

Mean Field Approximation in Conformation Dynamics

We propose a new approach to the transfer operator based analysis of the conformation dynamics of molecules. It is based on a statistical independence ansatz for the eigenfunctions of the operator related to a partitioning into subsystems. Numerical tests performed on small systems show excellent qualitative agreement between mean field and exact model, at greatly reduced computational cost.