# Interpretable Symbolic Regression for Data Science: Analysis of the 2022 Competition

arXiv: https://arxiv.org/abs/2304.01117 · HTML: https://mlsanity.com/paper/2304.01117/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 48 references that are in the map.
- First posted on arXiv 3 Apr 2023.

## Builds on (most cited first, 22 of 22)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Tabular Data: Deep Learning is Not All You Need](https://mlsanity.com/paper/2106.03253/) (2021)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison](https://mlsanity.com/paper/1703.00512/) (2017)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [PMLB v1.0: An open source dataset collection for benchmarking machine learning methods](https://mlsanity.com/paper/2012.00058/) (2020)
- [Where are we now? A large benchmark study of recent symbolic regression methods](https://mlsanity.com/paper/1804.09331/) (2018)
- [Fast, accurate, and transferable many-body interatomic potentials by symbolic regression](https://mlsanity.com/paper/1904.01095/) (2019)
- [An Approach to Symbolic Regression Using Feyn](https://mlsanity.com/paper/2104.05417/) (2021)
- [Taylor Genetic Programming for Symbolic Regression](https://mlsanity.com/paper/2205.09751/) (2022)
- [Learning a Formula of Interpretability to Learn Interpretable Formulas](https://mlsanity.com/paper/2004.11170/) (2020)
- [Complexity Measures for Multi-objective Symbolic Regression](https://mlsanity.com/paper/2109.00238/) (2021)
- [Automated Learning of Interpretable Models with Quantified Uncertainty](https://mlsanity.com/paper/2205.01626/) (2022)
- [Differentiable Genetic Programming](https://mlsanity.com/paper/1611.04766/) (2016)
- [Taskflow: A Lightweight Parallel and Heterogeneous Task Graph Computing System](https://mlsanity.com/paper/2004.10908/) (2020)
- [Data types as a more ergonomic frontend for Grammar-Guided Genetic Programming](https://mlsanity.com/paper/2210.04826/) (2022)

## Built on by (most cited first, 6 of 6)

- [Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl](https://mlsanity.com/paper/2305.01582/) (2023)
- [Symbolic Regression for Beyond the Standard Model Physics](https://mlsanity.com/paper/2405.18471/) (2024)
- [Unit-Aware Genetic Programming for the Development of Empirical Equations](https://mlsanity.com/paper/2405.18896/) (2024)
- [Discovering an interpretable mathematical expression for a full wind-turbine wake with artificial intelligence enhanced symbolic regression](https://mlsanity.com/paper/2406.00695/) (2024)
- [Symbolic Regression and Differentiable Fits in Beyond the Standard Model Physics](https://mlsanity.com/paper/2510.20453/) (2025)
- [Symbolic Classification-Enabled LHC Limits for BSM Global Fits](https://mlsanity.com/paper/2605.22330/) (2026)

## Abstract (arXiv)

Symbolic regression searches for analytic expressions that accurately describe studied phenomena. The main attraction of this approach is that it returns an interpretable model that can be insightful to users. Historically, the majority of algorithms for symbolic regression have been based on evolutionary algorithms. However, there has been a recent surge of new proposals that instead utilize approaches such as enumeration algorithms, mixed linear integer programming, neural networks, and Bayesian optimization. In order to assess how well these new approaches behave on a set of common challenges often faced in real-world data, we hosted a competition at the 2022 Genetic and Evolutionary Computation Conference consisting of different synthetic and real-world datasets which were blind to entrants. For the real-world track, we assessed interpretability in a realistic way by using a domain expert to judge the trustworthiness of candidate models.We present an in-depth analysis of the results obtained in this competition, discuss current challenges of symbolic regression algorithms and highlight possible improvements for future competitions.