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Identifying the mathematical relationships that best describe a dataset remains a very challenging problem in machine learning, and is known as Symbolic Regression (SR). In contrast to neural networks which are often treated as black boxes,…

Machine Learning · Computer Science 2023-01-10 Tony Tohme , Dehong Liu , Kamal Youcef-Toumi

The Symbolic Regression (SR) problem, where the goal is to find a regression function that does not have a pre-specified form but is any function that can be composed of a list of operators, is a hard problem in machine learning, both…

Machine Learning · Computer Science 2020-06-15 Vernon Austel , Cristina Cornelio , Sanjeeb Dash , Joao Goncalves , Lior Horesh , Tyler Josephson , Nimrod Megiddo

Symbolic Regression (SR) is a regression method that aims to discover mathematical expressions that describe the relationship between variables, and it is often implemented through Genetic Programming, a metaphor for the process of…

Neural and Evolutionary Computing · Computer Science 2025-12-02 Guilherme Seidyo Imai Aldeia

In Symbolic Regression (SR), Genetic Programming (GP) is a popular search algorithm that delivers state-of-the-art results in term of accuracy. Its success relies on the concept of neutrality, which induces large plateaus that the search…

Machine Learning · Computer Science 2025-11-04 Fabricio Olivetti de Franca , Gabriel Kronberger

Interpretability is crucial for machine learning in many scenarios such as quantitative finance, banking, healthcare, etc. Symbolic regression (SR) is a classic interpretable machine learning method by bridging X and Y using mathematical…

Methodology · Statistics 2020-01-17 Ying Jin , Weilin Fu , Jian Kang , Jiadong Guo , Jian Guo

Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. Such scenarios often require specific model properties such as interpretability, robustness,…

Symbolic regression (SR) is the problem of learning a symbolic expression from numerical data. Recently, deep neural models trained on procedurally-generated synthetic datasets showed competitive performance compared to more classical…

Machine Learning · Computer Science 2023-05-11 Pierre-Alexandre Kamienny , Guillaume Lample , Sylvain Lamprier , Marco Virgolin

Symbolic regression (SR) poses a significant challenge for randomized search heuristics due to its reliance on the synthesis of expressions for input-output mappings. Although traditional genetic programming (GP) algorithms have achieved…

Neural and Evolutionary Computing · Computer Science 2024-02-12 Kirill Antonov , Roman Kalkreuth , Kaifeng Yang , Thomas Bäck , Niki van Stein , Anna V Kononova

Symbolic regression (SR) is the task of learning a model of data in the form of a mathematical expression. By their nature, SR models have the potential to be accurate and human-interpretable at the same time. Unfortunately, finding such…

Neural and Evolutionary Computing · Computer Science 2022-07-12 Marco Virgolin , Solon P. Pissis

Genetic programming (GP) is a commonly used approach to solve symbolic regression (SR) problems. Compared with the machine learning or deep learning methods that depend on the pre-defined model and the training dataset for solving SR…

Neural and Evolutionary Computing · Computer Science 2022-05-23 Baihe He , Qiang Lu , Qingyun Yang , Jake Luo , Zhiguang Wang

Recently, several algorithms for symbolic regression (SR) emerged which employ a form of multiple linear regression (LR) to produce generalized linear models. The use of LR allows the algorithms to create models with relatively small error…

Machine Learning · Computer Science 2017-03-13 Jan Žegklitz , Petr Pošík

Symbolic regression (SR) is the process of discovering hidden relationships from data with mathematical expressions, which is considered an effective way to reach interpretable machine learning (ML). Genetic programming (GP) has been the…

Neural and Evolutionary Computing · Computer Science 2023-04-19 Peng Zeng , Xiaotian Song , Andrew Lensen , Yuwei Ou , Yanan Sun , Mengjie Zhang , Jiancheng Lv

The problem of symbolic regression (SR) arises in many different applications, such as identifying physical laws or deriving mathematical equations describing the behavior of financial markets from given data. Various methods exist to…

Artificial Intelligence · Computer Science 2025-05-07 Philipp Scholl , Katharina Bieker , Hillary Hauger , Gitta Kutyniok

Symbolic Regression (SR) algorithms attempt to learn analytic expressions which fit data accurately and in a highly interpretable manner. Conventional SR suffers from two fundamental issues which we address here. First, these methods search…

Cosmology and Nongalactic Astrophysics · Physics 2024-08-05 Deaglan J. Bartlett , Harry Desmond , Pedro G. Ferreira

Symbolic regression (SR) aims to discover concise closed-form mathematical equations from data, a task fundamental to scientific discovery. However, the problem is highly challenging because closed-form equations lie in a complex…

Machine Learning · Computer Science 2024-01-02 Samuel Holt , Zhaozhi Qian , Mihaela van der Schaar

Symbolic regression is the process of identifying mathematical expressions that fit observed output from a black-box process. It is a discrete optimization problem generally believed to be NP-hard. Prior approaches to solving the problem…

Neural and Evolutionary Computing · Computer Science 2021-11-19 T. Nathan Mundhenk , Mikel Landajuela , Ruben Glatt , Claudio P. Santiago , Daniel M. Faissol , Brenden K. Petersen

Symbolic regression (SR) has emerged as a powerful method for uncovering interpretable mathematical relationships from data, offering a novel route to both scientific discovery and efficient empirical modelling. This article introduces the…

Machine Learning · Computer Science 2026-04-10 Deaglan J. Bartlett , Harry Desmond , Pedro G. Ferreira , Gabriel Kronberger

Mathematical formulas are the crystallization of human wisdom in exploring the laws of nature for thousands of years. Describing the complex laws of nature with a concise mathematical formula is a constant pursuit of scientists and a great…

Machine Learning · Computer Science 2024-09-20 Yanjie Li , Jingyi Liu , Weijun Li , Lina Yu , Min Wu , Wenqiang Li , Meilan Hao , Su Wei , Yusong Deng

Symbolic regression (SR) is the task of discovering a symbolic expression that fits a given data set from the space of mathematical expressions. Despite the abundance of research surrounding the SR problem, there's a scarcity of works that…

Computational Complexity · Computer Science 2024-04-23 Jinglu Song , Qiang Lu , Bozhou Tian , Jingwen Zhang , Jake Luo , Zhiguang Wang

Symbolic regression (SR) is a powerful technique for discovering the analytical mathematical expression from data, finding various applications in natural sciences due to its good interpretability of results. However, existing methods face…

Machine Learning · Computer Science 2024-07-11 Xieting Chu , Hongjue Zhao , Enze Xu , Hairong Qi , Minghan Chen , Huajie Shao
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