Simple method for inference in inverse Ising problem using full data

Abstract

We consider inference in the inverse Ising problem using full data, which means incorporating sets of spin configurations. We approximate the Boltzmann distribution of the system to generate a frequency distribution derived from the given data. Then, the ratio between two Boltzmann distributions with different spin configurations eliminates the partition function and we obtain linear equations which can be solved to yield statistical parameters. Our method is applicable to cases where the absolute values of the coupling parameters and external fields are large. Compared to pseudolikelihood maximization, the accuracy of the inference obtained from our method is similar, although our approach is less labor intensive.