Symbolic Regression for Choice Models: An Interpretable Data-Driven Machine Learning for Discovering Utility Specifications

Abstract

This paper proposes symbolic regression (SR) as an interpretable, data-driven approach to utility specification in discrete choice models. The aim is to address the limitations of traditional manual specification search and the lack of interpretability in common machine learning methods. The methodology formulates the systematic utility difference as an unknown function learned via SR, optimised using a logit negative log-likelihood, ensuring consistency with random utility theory. SR generates a Pareto frontier of candidate specifications, balancing goodness-of-fit and complexity. Using synthetic binary choice data, we evaluate the ability of SR to recover known functional forms under varying search spaces, including missing transformations, irrelevant features, and noise variables. The results show that SR consistently recovers the true specification, reconstructs nonlinear effects endogenously, and remains robust to irrelevant inputs. These findings demonstrate the potential of SR to support systematic, interpretable specification discovery in choice modelling.