The Inverse Ising Problem

The inverse Ising problem consists of taking a set of Ising configurations generated with unknown interaction parameters, and deter- mining reliable estimates for the values of those interaction parameters. The problem first arose in connection with the Monte Carlo renormalization group, and was solved thirty years ago. Recently, there has been renewed interest in the inverse Ising problem due to biological applications. The original solution seems to have been forgotten, as it was rediscovered in a different representation by Aurell and Ekeberg in 2012. In this paper we modify the earlier equations to solve problems that are not translationally invariant.