Parameter identification for symbolic regression using nonlinear least squares
Parameter identification for symbolic regression using nonlinear least squares
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DOI：
10.1007/s10710-019-09371-3
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发表时间：
2019-12-10
影响因子：
2.6
通讯作者：
Affenzeller, Michael
中科院分区：
文献类型：
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作者：
Kommenda, Michael;Burlacu, Bogdan;Affenzeller, Michael
在本文中，我们分析了使用非线性最小二乘符合符号回归模型的参数识别的效果，并将其作为基于树的遗传编程中的局部搜索机制集成为局部搜索机制。我们采用Levenberg-Marquardt算法进行参数优化，并通过自动分化来计算梯度。我们提供参数识别成功并失败并突出其计算开销的示例。使用广泛的符号回归基准问题套件，当将非线性最小二乘在遗传编程中纳入时，我们证明了性能的提高。将我们的结果与通过几种基因编程变体和最先进的机器学习算法获得的最近发布的结果进行了比较。使用非线性最小二乘正方形的遗传编程在定义的基准套件上的最佳措施中，只要在模型中仅使用可区分的功能，就可以轻松地将本地搜索集成到不同的遗传编程算法中。
In this paper we analyze the effects of using nonlinear least squares for parameter identification of symbolic regression models and integrate it as local search mechanism in tree-based genetic programming. We employ the Levenberg-Marquardt algorithm for parameter optimization and calculate gradients via automatic differentiation. We provide examples where the parameter identification succeeds and fails and highlight its computational overhead. Using an extensive suite of symbolic regression benchmark problems we demonstrate the increased performance when incorporating nonlinear least squares within genetic programming. Our results are compared with recently published results obtained by several genetic programming variants and state of the art machine learning algorithms. Genetic programming with nonlinear least squares performs among the best on the defined benchmark suite and the local search can be easily integrated in different genetic programming algorithms as long as only differentiable functions are used within the models.