# A Probabilistic Linear Genetic Programming with Stochastic Context-Free Grammar for solving Symbolic Regression problems

arXiv: https://arxiv.org/abs/1704.00828 · HTML: https://mlsanity.com/paper/1704.00828/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2017.

## Built on by (most cited first, 3 of 3)

- [A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge](https://mlsanity.com/paper/2209.06257/) (2022)
- [Symbolic Regression as Feature Engineering Method for Machine and Deep Learning Regression Tasks](https://mlsanity.com/paper/2311.06028/) (2023)
- [A Reinforcement Learning Approach to Domain-Knowledge Inclusion Using Grammar Guided Symbolic Regression](https://mlsanity.com/paper/2202.04367/) (2022)

## Abstract (arXiv)

Traditional Linear Genetic Programming (LGP) algorithms are based only on the selection mechanism to guide the search. Genetic operators combine or mutate random portions of the individuals, without knowing if the result will lead to a fitter individual. Probabilistic Model Building Genetic Programming (PMB-GP) methods were proposed to overcome this issue through a probability model that captures the structure of the fit individuals and use it to sample new individuals. This work proposes the use of LGP with a Stochastic Context-Free Grammar (SCFG), that has a probability distribution that is updated according to selected individuals. We proposed a method for adapting the grammar into the linear representation of LGP. Tests performed with the proposed probabilistic method, and with two hybrid approaches, on several symbolic regression benchmark problems show that the results are statistically better than the obtained by the traditional LGP.