Incorporating background knowledge in symbolic regression using a computer algebra system

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 ex...

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Bibliographic Details
Published in:Machine learning: science and technology 2024-06, Vol.5 (2), p.025057
Main Authors: Fox, Charles, Tran, Neil D, Nacion, F Nikki, Sharlin, Samiha, Josephson, Tyler R
Format: Article
Language:English
Subjects:
adsorption
Bayesian
Bayesian analysis
Computer algebra
Datasets
Genetic algorithms
Markov chains
symbolic regression
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Summary: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 incorporating these constraints in Bayesian SR (as the Bayesian prior) is better than by modifying the fitness function in the GA.
ISSN:2632-2153
2632-2153
DOI:10.1088/2632-2153/ad4a1e