Space Dependent Mean Field Approximation Modelling

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.

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.

Online Mean Field Approximation for Automated Experimentation

In this paper, we propose a semi-supervised online graph labelling method that a↵ords early learning capability. We use mean field approximation for predicting the unknown labels of the vertices of the graph with high accuracy on the standard benchmark datasets. The minimum cut is the energy function of our probabilistic model that encodes the uncertainty about the labels of the vertices. Our m...