Adaptive Cluster Expansion for the Inverse Ising Problem: Convergence, Algorithm and Tests

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 spins, 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.