Variational phasor mean field model for Markov random fields

We show that a variational phasor mean field approximation for Markov random fields can well represent marginal distribution as well as correlation among the sites. The network is represented by complex valued equations, which consist of phase equations and variational mean-field equations; the correlation coefficient between two sites on stochastic machines can be given by the cosine of the phase differences. This enables to compute the correlation between two units directly in a deterministic manner. The variational correlation network improves the accuracy of the mean field approximation for graphical models. Unlike the conventional elaborated mean field methods the efficient training method can be implemented on this model. The model gives a much more efficient learning recipe for pattern recognition or image processing than Markov network models.