Bayesian Inference Based on Stationary Fokker-Planck Sampling

A novel formalism for Bayesian learning in the context of complex inference models is proposed. The method is based on the use of Stationary Fokker--Planck (SFP) sampling in order to sample from the posterior density. The SFP procedure admits the construction of approximate analytical expressions for the marginals of the posterior. Off--line and on--line Bayesian inference and Maximum Likelihood Estimation from the posterior is performed in classification and regression examples. The computation cost of SFP, measured in terms of loss function evaluations, grows linearly with the inference model's dimension.