  Mean-Field is an efficient way to approximate a posterior distribution in
complex graphical models and constitutes the most popular class of Bayesian
variational approximation methods. In most applications, the mean field
distribution parameters are computed using an alternate coordinate
minimization. However, the convergence properties of this algorithm remain
unclear. In this paper, we show how, by adding an appropriate penalization
term, we can guarantee convergence to a critical point, while keeping a closed
form update at each step. A convergence rate estimate can also be derived based
on recent results in non-convex optimization.
