Symbolic regression: Difference between revisions

Revision as of 07:57, 7 July 2022

Revision as of 13:59, 10 July 2022

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By not requiring ''a priori'' specification of a model, symbolic regression isn't affected by human bias, or unknown gaps in [[___domain knowledge]]. It attempts to uncover the intrinsic relationships of the dataset, by letting the patterns in the data itself reveal the appropriate models, rather than imposing a model structure that is deemed mathematically tractable from a human perspective. The [[fitness function]] that drives the evolution of the models takes into account not only [[Residual (numerical analysis)|error metrics]] (to ensure the models accurately predict the data), but also special complexity measures,<ref name="complexity"/> thus ensuring that the resulting models reveal the data's underlying structure in a way that's understandable from a human perspective. This facilitates reasoning and favors the odds of getting insights about the data-generating system.

It has been proven that symbolic regression is an [[NP-hardness|NP-hard]] problem, in the sense that one cannot always find the best possible mathematical expression to fit to a given dataset in [[Polynomial-time|polynomial time]].<ref>{{Cite journal |lastlast1=Virgolin |firstfirst1=Marco |last2=Pissis |first2=Solon P. |date=2022-07-05 |title=Symbolic Regression is NP-hard |url=http://arxiv.org/abs/2207.01018 |journalarxiv=arXiv:2207.01018 [cs]}}</ref>

== Difference from classical regression ==

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=== End-user software ===

* [[dCGP]], differentiable Cartesian Genetic Programming in python (free, open source) <ref>{{Cite web|url=https://darioizzo.github.io/dcgp/|title=Differentiable Cartesian Genetic Programming, v1.6 Documentation|date=June 10, 2022}}</ref><ref>{{Cite journal|title=Differentiable genetic programming|first1=Dario|last1=Izzo|first2=Francesco|last2=Biscani|first3=Alessio|last3=Mereta|journal=Proceedings of the European conferenceConference on geneticGenetic Programming|year=2016 programming|arxiv=1611.04766 }}</ref>

* [[HeuristicLab]], a software environment for heuristic and evolutionary algorithms, including symbolic regression (free, open source)

* [[Gene expression programming#Software|GeneXProTools]], - an implementation of [[Gene expression programming]] technique for various problems including symbolic regression (commercial)