Adaptive TAP Equations
Manfred Opper, Ole Winther · The MIT Press eBooks · 2001
Introduction Mean field (MF) methods provide efficient approximations which are able to cope with the increasing complexity of modern probabilistic data models. They replace the intractable task of computing high dimensional sums and integrals by the tractable problem of solving a system of nonlinear equations. The TAP (21) MF approach represents a principled way for correcting the deficiencies of simple MF methods which are based on the crude approximation of replacing the intractable distribution by a factorized one, thereby neglecting important correlations between variables. In contrast, the TAP method takes into account nontrivial dependencies by estimating the reaction of all other random variables when a single variable is deleted from the system (8). The method has its origin in the statistical physics of amorphous systems, where it was developed by Thouless, Anderson and Palmer (TAP) to treat the Sherrington-Kirkpatrick (SK) model of disordered magnetic materials (19)