A Refined Mean Field Approximation for Synchronous Population Processes

A Mean Field Approximation of the Bolker-Pacala Population Model

We approximate the Bolker-Pacala model of population dynamics with the logistic Markov chain and analyze the latter. We find the asymptotics of the degenerated hypergeometric function and use these to prove a local CLT and large deviations result. We also state global limit theorems and obtain asymptotics for the first passage time to the boundary of a large interval.

A weak approximation for the Extrema's distributions of Levy processes

‎Suppose that $X_{t}$ is a one-dimensional and real-valued L'evy‎ ‎process started from $X_0=0$‎, ‎which ({bf 1}) its nonnegative‎ ‎jumps measure $nu$ satisfying $int_{Bbb‎ ‎R}min{1,x^2}nu(dx)

Mean Field Approximation for Fields of Experts

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...

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.