Priors for symbolic regression

Conference item

When choosing between competing symbolic models for a data set, a human will naturally prefer the “simpler” expression or the one which more closely resembles equations previously seen in a similar context. This suggests a non-uniform prior on functions, which is, however, rarely considered within a symbolic regression (SR) framework. In this paper we develop methods to incorporate detailed prior information on both functions and their parameters into SR. Our prior on the structure of a function is based on a ngram language model, which is sensitive to the arrangement of operators relative to one another in addition to the frequency of occurrence of each operator. We also develop a formalism based on the Fractional Bayes Factor to treat numerical parameter priors in such a way that models may be fairly compared though the Bayesian evidence, and explicitly compare Bayesian, Minimum Description Length and heuristic methods for model selection. We demonstrate the performance of our priors relative to literature standards on benchmarks and a real-world dataset from the field of cosmology.

Authors: Bartlett, D; Desmond, H; Ferreira, P

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Association for Computing Machinery
• Host title: GECCO '23 Companion: Proceedings of the Companion Conference on Genetic and Evolutionary Computation
• Pages: 2402-2411
• Publication date: 2023-07-24
• Event title: Companion Conference on Genetic and Evolutionary Computation (GECCO 2023)
• Event location: Lisbon, Portugal
• Event website: https://gecco-2023.sigevo.org/HomePage.html
• Event start date: 2023-07-15
• Event end date: 2023-07-19
• DOI: 10.1145/3583133.3596327
• ISBN: 9798400701207
• Language: English
• Keywords: model selection; minimum description length; symbolic regression; equation learning; data analysis; cosmology; language model