Variational Bayes and Mean Field Approximations for Markov field unsupervised estimation

We consider the problem of parameter estimation of Markovian models where the exact computation of the partition function is not possible or computationally too expensive with MCMC methods. The main idea is then to approximate the expression of the likelihood by a simpler one where we can either have an analytical expression or compute it more efficiently. We consider two approaches: Variational Bayes Approximation (VBA) and Mean Field Approximation (MFA) and study the properties of such approximations and their effects on the estimation of the parameters.