Inferring the fields and couplings of an Ising model from the set of
its magnetizations and pairwise correlations is an important problem
in information theory, statistics, and physics. We propose an
inference algorithm based on a recursive calculation of the
multi-spins contributions to the Ising entropy. The recursive
procedure is pruned to prevent the outcome from being corrupted by 
the noise present in the data. The algorithm is applied to real data
coming from neurobiology experiments, and compared to existing
algorithms developed in information theory and statistics 
communities.