Symbolic Regression using Mixed-Integer Nonlinear Optimization
This addresses the computationally hard problem of symbolic regression for researchers and practitioners, but it is incremental as it builds on existing mathematical programming approaches.
The authors tackled the Symbolic Regression problem by proposing a hybrid algorithm combining mixed-integer nonlinear optimization with explicit enumeration and dimensional analysis constraints, showing it is competitive with state-of-the-art methods like AI Feynman on some synthetic datasets.
The Symbolic Regression (SR) problem, where the goal is to find a regression function that does not have a pre-specified form but is any function that can be composed of a list of operators, is a hard problem in machine learning, both theoretically and computationally. Genetic programming based methods, that heuristically search over a very large space of functions, are the most commonly used methods to tackle SR problems. An alternative mathematical programming approach, proposed in the last decade, is to express the optimal symbolic expression as the solution of a system of nonlinear equations over continuous and discrete variables that minimizes a certain objective, and to solve this system via a global solver for mixed-integer nonlinear programming problems. Algorithms based on the latter approach are often very slow. We propose a hybrid algorithm that combines mixed-integer nonlinear optimization with explicit enumeration and incorporates constraints from dimensional analysis. We show that our algorithm is competitive, for some synthetic data sets, with a state-of-the-art SR software and a recent physics-inspired method called AI Feynman.