  The chief aim of this paper is to propose mean-field approximations for a
broad class of Belief networks, of which sigmoid and noisy-or networks can be
seen as special cases. The approximations are based on a powerful mean-field
theory suggested by Plefka. We show that Saul, Jaakkola and Jordan' s approach
is the first order approximation in Plefka's approach, via a variational
derivation. The application of Plefka's theory to belief networks is not
computationally tractable. To tackle this problem we propose new approximations
based on Taylor series. Small scale experiments show that the proposed schemes
are attractive.
