TAP Gibbs Free Energy, Belief Propagation and Sparsity

The adaptive TAP Gibbs free energy for a general densely connected probabilistic model with quadratic interactions and arbritary single site constraints is derived. We show how a specific sequential minimization of the free energy leads to a generalization of Minka's expectation propa- gation. Lastly, we derive a sparse representation version of the sequential algorithm. The usefulness of the approach is demonstrated on classifica- tion and density estimation with Gaussian processes and on an indepen- dent component analysis problem.