"We present a procedure to solve the inverse Ising problem, that is to find the interactions between a set of binary variables from the measure of their equilibrium correlations. The method consists in constructing and selecting specific clusters of variables, based on their contributions to the cross-entropy of the Ising model. Small contributions are discarded to avoid overfitting and to make the computation tractable. The properties of the cluster expansion and its performances on synthetic data are studied. To make the implementation easier we give the pseudo-code of the algorithm."

"The inverse Ising problem is a difficult combinatorial optimization problem in the class known as “NP-hard”. In theory, only approximate schemes, or methods that take more than polynomial time to find the answer are possible. Boltzmann Learning [1] is an iterative method where in one step the correlation functions are computed given an Ising model, and in another step the Ising model couplings are modified to adjust to data. In principle, Boltzmann learning can be employed to find the couplings with arbi- trary accuracy given accurate data and sufficient time, but the slow convergence of the Boltzmann learning makes it a very inefficient algorithm for most practical purposes."