research-article

Priors for symbolic regression

Authors:

Deaglan Bartlett,

Pedro FerreiraAuthors Info & Claims

GECCO '23 Companion: Proceedings of the Companion Conference on Genetic and Evolutionary Computation

Pages 2402 - 2411

https://doi.org/10.1145/3583133.3596327

Published: 24 July 2023 Publication History

Abstract

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 n-gram 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.

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Cited By

Leser PBomarito GKronberger GOlivetti De França FLi XHandl J(2024)Comparing Methods for Estimating Marginal Likelihood in Symbolic RegressionProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3638530.3664142(2058-2066)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638530.3664142
Sousa TBartlett DDesmond HFerreira P(2024)Optimal inflationary potentialsPhysical Review D10.1103/PhysRevD.109.083524109:8Online publication date: 18-Apr-2024
https://doi.org/10.1103/PhysRevD.109.083524
Bartlett DWandelt BZennaro MFerreira PDesmond H(2024)SYREN-HALOFIT: A fast, interpretable, high-precision formula for the ΛCDM nonlinear matter power spectrumAstronomy & Astrophysics10.1051/0004-6361/202449854686(A150)Online publication date: 5-Jun-2024
https://doi.org/10.1051/0004-6361/202449854

Index Terms

Priors for symbolic regression
1. Computing methodologies
  1. Machine learning
2. Mathematics of computing
  1. Probability and statistics
    1. Probabilistic inference problems

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GECCO '23 Companion: Proceedings of the Companion Conference on Genetic and Evolutionary Computation

July 2023

2519 pages

ISBN:9798400701207

DOI:10.1145/3583133

Chair:
Sara Silva,
Program Chair:
Luís Paquete

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Leser PBomarito GKronberger GOlivetti De França FLi XHandl J(2024)Comparing Methods for Estimating Marginal Likelihood in Symbolic RegressionProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3638530.3664142(2058-2066)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638530.3664142
Sousa TBartlett DDesmond HFerreira P(2024)Optimal inflationary potentialsPhysical Review D10.1103/PhysRevD.109.083524109:8Online publication date: 18-Apr-2024
https://doi.org/10.1103/PhysRevD.109.083524
Bartlett DWandelt BZennaro MFerreira PDesmond H(2024)SYREN-HALOFIT: A fast, interpretable, high-precision formula for the ΛCDM nonlinear matter power spectrumAstronomy & Astrophysics10.1051/0004-6361/202449854686(A150)Online publication date: 5-Jun-2024
https://doi.org/10.1051/0004-6361/202449854

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