# 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…

## 34 Citations

### GSR: A Generalized Symbolic Regression Approach

- Computer ScienceArXiv
- 2022

This paper presents GSR, a Generalized Symbolic Regression approach, by modifying the conventional SR optimization problem formulation, while keeping the main SR objective intact, and proposes a genetic programming approach with a matrix-based encoding scheme.

### Exhaustive Symbolic Regression

- Computer ScienceArXiv
- 2022

A new method is introduced – Exhaustive Symbolic Regression (ESR) – which systematically and efﬁciently considers all possible equations and is therefore guaranteed to be not only the true optimum but also a complete function ranking.

### Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery

- Computer ScienceArXiv
- 2022

This paper revisits datasets and evaluation criteria for Symbolic Regression, a task of recovering mathematical expressions from given data, and proposes to use normalized edit distances between a predicted equation and the ground-truth equation trees as an evaluation metric.

### Symbolic Regression is NP-hard

- Computer ScienceArXiv
- 2022

Evidence suggesting that the answer to the question: Is there an exact polynomial-time algorithm to compute SR models is probably negative is provided by showing that SR is NP-hard.

### Taylor genetic programming for symbolic regression

- Computer ScienceGECCO
- 2022

This work proposes a new method for SR, called Taylor genetic programming (TaylorGP), which leverages a Taylor polynomial to approximate the symbolic equation that fits the dataset and utilizes the Taylor poynomial to extract the features of the symbolic equations.

### End-to-end symbolic regression with transformers

- Computer ScienceArXiv
- 2022

This paper challenges this two-step procedure, and task a Transformer to directly predict the full mathematical expression, constants included, and presents ablations to show that this end-to-end approach yields better results, sometimes even without the refinement step.

### Symbolic Expression Transformer: A Computer Vision Approach for Symbolic Regression

- Computer ScienceArXiv
- 2022

This work proposes Symbolic Expression Transformer (SET), a sample-agnostic model from the perspective of computer vision for SR, and demonstrates the effectiveness and suggests the promising direction of image-based model for solving the challenging SR problem.

### Interpretability in symbolic regression: a benchmark of explanatory methods using the Feynman data set

- Computer ScienceGenetic Programming and Evolvable Machines
- 2022

A benchmark scheme to evaluate explanatory methods to explain regression models, mainly symbolic regression models and observed that Partial Effects and SHAP were the most robust explanation models, with Integrated Gradients being unstable only with tree-based models.

### SciMED: A Computational Framework For Physics-Informed Symbolic Regression with Scientist-In-The-Loop

- Computer ScienceArXiv
- 2022

A novel, open-source computational framework called Scientist-Machine Equation Detector (SciMED), which integrates scientiﬁc discipline wisdom in a scientist-in- the-loop approach with state-of-the-art symbolic regression (SR) methods.

### Transformation-interaction-rational representation for symbolic regression

- Computer ScienceProceedings of the Genetic and Evolutionary Computation Conference
- 2022

An extension to this representation, called Transformation-Interaction-Rational representation, is proposed that defines a new function form as the rational of two Interaction-Transformation functions, and the target variable can also be transformed with an univariate function.

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