Incorporating Background Knowledge in Symbolic Regression using a Computer Algebra System
This work addresses the challenge of making symbolic regression more interpretable and theory-consistent for researchers in fields like materials science, though it is incremental as it builds on existing methods like genetic algorithms and Bayesian approaches.
The paper tackled the problem of incorporating background knowledge as symbolic constraints into symbolic regression to generate more meaningful and interpretable expressions, finding that soft constraints improve search effectiveness and model meaningfulness while increasing computational costs by about an order-of-magnitude.
Symbolic Regression (SR) can generate interpretable, concise expressions that fit a given dataset, allowing for more human understanding of the structure than black-box approaches. The addition of background knowledge (in the form of symbolic mathematical constraints) allows for the generation of expressions that are meaningful with respect to theory while also being consistent with data. We specifically examine the addition of constraints to traditional genetic algorithm (GA) based SR (PySR) as well as a Markov-chain Monte Carlo (MCMC) based Bayesian SR architecture (Bayesian Machine Scientist), and apply these to rediscovering adsorption equations from experimental, historical datasets. We find that, while hard constraints prevent GA and MCMC SR from searching, soft constraints can lead to improved performance both in terms of search effectiveness and model meaningfulness, with computational costs increasing by about an order-of-magnitude. If the constraints do not correlate well with the dataset or expected models, they can hinder the search of expressions. We find Bayesian SR is better these constraints (as the Bayesian prior) than by modifying the fitness function in the GA