Automatic identification of hierarchy in multivariate data

Given n variables to model, symbolic regression (SR) returns a flat list of n equations. As the number of state variables to be modeled scales, it becomes increasingly difficult to interpret such a list. Here we present a symbolic regression method that detects and captures hidden hierarchy in a given system. The method returns the equations in a hierarchical dependency graph, which increases the interpretability of the results. We demonstrate two variations of this hierarchical modeling approach, and show that both consistently outperform non-hierarchical symbolic regression on a number of synthetic data sets.