  We introduce a new cluster-cumulant expansion (CCE) based on the fixed points
of iterative belief propagation (IBP). This expansion is similar in spirit to
the loop-series (LS) recently introduced in [1]. However, in contrast to the
latter, the CCE enjoys the following important qualities: 1) it is defined for
arbitrary state spaces 2) it is easily extended to fixed points of generalized
belief propagation (GBP), 3) disconnected groups of variables will not
contribute to the CCE and 4) the accuracy of the expansion empirically improves
upon that of the LS. The CCE is based on the same M\"obius transform as the
Kikuchi approximation, but unlike GBP does not require storing the beliefs of
the GBP-clusters nor does it suffer from convergence issues during belief
updating.
