- author = "William {La Cava} and Patryk Orzechowski and Bogdan Burlacu and Fabricio {de Franca} and Marco Virgolin and Ying Jin and Michael Kommenda and Jason Moore",
- title = "Contemporary Symbolic Regression Methods and their Relative Performance",
- booktitle = "Proceedings of the Neural Information Processing Systems Track on Datasets and Benchmarks",
- year = "2021",
- editor = "Joaquin Vanschoren and Sai-Kit Yeung",
- volume = "1",
- publisher = "Curran",
- keywords = "genetic algorithms, genetic programming, model interpretability, XAI, ANN, Eureqa, SRbench, Markov Chain Monte Carlo, MCMC, Python, Random Forest, AdaBoost",
-
URL = "
https://datasets-benchmarks-proceedings.neurips.cc/paper/2021/hash/c0c7c76d30bd3dcaefc96f40275bdc0a-Abstract-round1.html",
-
URL = "
https://datasets-benchmarks-proceedings.neurips.cc/paper/2021/file/c0c7c76d30bd3dcaefc96f40275bdc0a-Paper-round1.pdf",
-
URL = "https://arxiv.org/abs/2107.14351",
-
video_url = "https://nips.cc/virtual/2021/datasets-and-benchmarks/38447#collapse-sl-22748",
-
code_url = "https://github.com/cavalab/srbench",
-
data_url = "https://epistasislab.github.io/pmlb/",
- size = "16 pages",
- abstract = "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. In this paper, 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 known model form as well as ground-truth benchmark problems, including physics equations and systems of ordinary differential equations. For the real-world datasets, we benchmark the ability of each method to learn models with low error and low complexity relative to state-of-the-art machine learning methods. For the synthetic problems, we assess each method ability to find exact solutions in the presence of varying levels of noise. Under these controlled experiments, we conclude that the best performing methods for real-world regression combine genetic algorithms with parameter estimation and/or semantic search drivers. When tasked with recovering exact equations in the presence of noise, we find that deep learning and genetic algorithm-based approaches perform similarly. We provide a detailed guide to reproducing this experiment and contributing new methods, and encourage other researchers to collaborate with us on a common and living symbolic regression benchmark.",
-
notes = "Also known as \cite{NEURIPS DATASETS AND
BENCHMARKS2021_c0c7c76d}
SR bench github/pull based, hundreds of problems. Penn Machine Learning Benchmark PMLB
p3 'Eureqa ... we implement its underlying algorithms in an open-source package'
p4 'We required contributors to implement a minimal, Scikit-learn compatible, Python API ... compatible with ... https://www.sympy.org/en/index.html ... [must] be managed via www.anaconda.com/'
Table 2 'Computing budget: 1290000 core hours, 436800 core hours' (total 197 core years).
'Semantic backpropagation (SBP)...affine transformations'
'FFX \cite{McConaghy:2011:GPTP} simply initializes a population of equations, selects the Pareto optimal set, and returns a single linear model by treating the population of equations as features.'
p7 'Feynman Symbolic Regression Database, and the ODE-Strogatz repository'
{+, −, ∗, /, sin, cos, arcsin, arccos, exp, log, pow, max, min}. also 'simplifying via sympy'.
p8 'models generated by Operon are significantly more accurate' ... 'models produced by FEAT are significantly smaller'.
p19 'Operon C++ \cite{Kommenda:GPEM}, GP-GOMEA \cite{Virgolin:EC}, and DSR \cite{Petersen:2020:ICLR}, , which taken together give the set of best trade-offs between accuracy and simplicity across the black-box regression problems'
See also \cite{dick:2022:SymReg}
Also known as \cite{NEURIPS DATASETS AND BENCHMARKS2021_c0c7c76d} \cite{DBLP:journals/corr/abs-2107-14351},",
