Higher-order interactions in statistical physics and machine learning: A model-independent solution to the inverse problem at equilibrium.

The problem of inferring pairwise and higher-order interactions in complex systems involving large numbers of interacting variables, from observational data, is fundamental to many fields. Known to the statistical physics community as the inverse problem, it has become accessible in recent years due to real and simulated big data being generated. Current approaches to the inverse problem rely on parametric assumptions, physical approximations, e.