• Corpus ID: 236635250

Contemporary Symbolic Regression Methods and their Relative Performance

@article{Cava2021ContemporarySR,
  title={Contemporary Symbolic Regression Methods and their Relative Performance},
  author={W. L. Cava and Patryk Orzechowski and Bogdan Burlacu and Fabr'icio Olivetti de Francca and M. Virgolin and Ying Jin and Michael Kommenda and Jason H. Moore},
  journal={ArXiv},
  year={2021},
  volume={abs/2107.14351}
}
Many promising approaches to symbolic regression have been presented in recent years, yet progress in the field continues to suffer from a lack of uniform, robust, and transparent benchmarking standards. We address this shortcoming by introducing an open-source, reproducible benchmarking platform for symbolic regression. We assess 14 symbolic regression methods and 7 machine learning methods on a set of 252 diverse regression problems. Our assessment includes both real-world datasets with no… 

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  • F. O. de Franca
  • Computer Science
    Proceedings of the Genetic and Evolutionary Computation Conference
  • 2022
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References

SHOWING 1-10 OF 95 REFERENCES

Benchmarking state-of-the-art symbolic regression algorithms

This paper conceptually and experimentally compare several representatives of multiple linear regression algorithms, including GPTIPS, FFX, and EFS, which are applied as off-the-shelf, ready-to-use techniques in the field of SR.

Where are we now?: a large benchmark study of recent symbolic regression methods

The results suggest that symbolic regression performs strongly compared to state-of-the-art gradient boosting algorithms, although in terms of running times is among the slowest of the available methodologies.

FFX: Fast, Scalable, Deterministic Symbolic Regression Technology

A new non-evolutionary technique for symbolic regression that is orders of magnitude faster than competent GP approaches on real-world problems, returns simpler models, has comparable or better prediction on unseen data, and converges reliably and deterministically.

Improving Model-Based Genetic Programming for Symbolic Regression of Small Expressions

This article shows that the non-uniformity in the distribution of the genotype in GP populations negatively biases LL, and proposes a method to correct this, and finds that GOMEA is a promising new approach to SR.

PMLB: a large benchmark suite for machine learning evaluation and comparison

It is found that existing benchmarks lack the diversity to properly benchmark machine learning algorithms, and there are several gaps in benchmarking problems that still need to be considered.

Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients

The proposed framework uses a recurrent neural network to emit a distribution over tractable mathematical expressions, and employs reinforcement learning to train the network to generate better-fitting expressions, which significantly outperforms standard genetic programming-based symbolic regression in its ability to exactly recover symbolic expressions.

Pareto-Front Exploitation in Symbolic Regression

This work prefers parsimonious (simple) expressions with the expectation that they are more robust with respect to changes over time in the underlying system or extrapolation outside the range of the data used as the reference in evolving the symbolic regression.

Feature standardisation and coefficient optimisation for effective symbolic regression

It is demonstrated that standardisation allows a simpler function set to be used without increasing bias and can significantly improve the performance of coefficient optimisation through gradient descent to produce accurate models.

AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity

We present an improved method for symbolic regression that seeks to fit data to formulas that are Pareto-optimal, in the sense of having the best accuracy for a given complexity. It improves on the

AI Feynman: A physics-inspired method for symbolic regression

This work develops a recursive multidimensional symbolic regression algorithm that combines neural network fitting with a suite of physics-inspired techniques and improves the state-of-the-art success rate.
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