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We present a physically transparent and computationally efficient method for obtaining cluster expansion coefficients in ab initio thermodynamics of multicomponent lattice-gas systems without any preconceived assumptions on the compactness of the cluster set or on the decay behavior of the interactions. The lowest possible cross-validation score for given input data is approximated by minimizing the fluctuations of the expansion coefficients, thus ensuring the transferability of the effective cluster interactions to arbitrary alloy configurations. The method is illustrated for bcc-based Fe-Co intermetallic alloys.