  We develop an advanced mean field method for approximating averages in
probabilistic data models that is based on the TAP approach of disorder
physics. In contrast to conventional TAP, where the knowledge of the
distribution of couplings between the random variables is required, our method
adapts to the concrete couplings. We demonstrate the validity of our approach,
which is sofar restricted to models with non-glassy behaviour, by replica
calculations for a wide class of models as well as by simulations for a real
data set.
