Prove Symbolic Regression is NP-hard by Symbol Graph

Jinglu Song; Qiang Lu; Bozhou Tian; Jingwen Zhang; Jake Luo; Zhiguang Wang

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arXiv · 2404.13820

Prove Symbolic Regression is NP-hard by Symbol Graph

Jinglu Song·Qiang Lu·Bozhou Tian·Jingwen Zhang·Jake Luo·Zhiguang Wang

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Abstract

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 confirm its NP-hard nature. Therefore, this paper introduces the concept of a symbol graph as a comprehensive representation of the entire mathematical expression space, effectively illustrating the NP-hard characteristics of the SR problem. Leveraging the symbol graph, we establish a connection between the SR problem and the task of identifying an optimally fitted degree-constrained Steiner Arborescence (DCSAP). The complexity of DCSAP, which is proven to be NP-hard, directly implies the NP-hard nature of the SR problem.

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Jinglu Song, Qiang Lu, Bozhou Tian, Jingwen Zhang, Jake Luo, Zhiguang Wang. 2024-04-22. Prove Symbolic Regression is NP-hard by Symbol Graph. https://arxiv.org/abs/2404.13820

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