Mean Field Theory for Sigmoid Belief Networks
  We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics. Our mean field theory provides a tractable approximation to the true probability distribution in these networks; it also yields a lower bound on the likelihood of evidence. We demonstrate the utility of this framework on a benchmark problem in statistical pattern recognition---the classification of handwritten digits. 
L. K. Saul, T. Jaakkola, M. I. Jordan