  We introduce a procedure to infer the interactions among a set of binary
variables, based on their sampled frequencies and pairwise correlations. The
algorithm builds the clusters of variables contributing most to the entropy of
the inferred Ising model, and rejects the small contributions due to the
sampling noise. Our procedure successfully recovers benchmark Ising models even
at criticality and in the low temperature phase, and is applied to
neurobiological data.
