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arXiv 2306.08057cs.NEcs.AIcs.LG

基于控制变量遗传编程的符号回归

Symbolic Regression via Control Variable Genetic Programming

Purdue University（普渡大学）

Nan Jiang, Yexiang Xue

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AI总结：

针对多自变量符号回归难题，受科学控制变量实验启发提出CVGP方法，通过增量式变量引入与定制实验设计缩减搜索空间，理论与实验均验证其优于现有基线。

摘要：

从实验数据中直接学习符号表达式是AI驱动科学发现的关键步骤。然而，当前最先进的方法仅能学习简单表达式，对包含多个自变量的表达式进行回归仍难以实现。受科学领域广泛应用的控制变量实验启发，我们提出控制变量遗传编程（CVGP），用于处理多自变量的符号回归任务。CVGP通过定制化实验设计加速符号表达式发现，而非从预先收集的固定数据集学习。它首先在其他变量保持为常数的控制实验中，用遗传编程拟合包含少量自变量的简单表达式；随后通过开展允许新增自变量变化的新控制变量实验，加入新自变量以扩展前代学习到的表达式。理论上，我们证明CVGP作为一种增量构建方法，在学习一类表达式时可使搜索空间呈指数级缩减。实验表明，在学习含多个自变量的符号表达式任务上，CVGP性能优于若干基线方法。

英文摘要：

Learning symbolic expressions directly from experiment data is a vital step in AI-driven scientific discovery. Nevertheless, state-of-the-art approaches are limited to learning simple expressions. Regressing expressions involving many independent variables still remain out of reach. Motivated by the control variable experiments widely utilized in science, we propose Control Variable Genetic Programming (CVGP) for symbolic regression over many independent variables. CVGP expedites symbolic expression discovery via customized experiment design, rather than learning from a fixed dataset collected a priori. CVGP starts by fitting simple expressions involving a small set of independent variables using genetic programming, under controlled experiments where other variables are held as constants. It then extends expressions learned in previous generations by adding new independent variables, using new control variable experiments in which these variables are allowed to vary. Theoretically, we show CVGP as an incremental building approach can yield an exponential reduction in the search space when learning a class of expressions. Experimentally, CVGP outperforms several baselines in learning symbolic expressions involving multiple independent variables.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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