论文标题
符号回归的转换相互作用理性表示
Transformation-Interaction-Rational Representation for Symbolic Regression
论文作者
论文摘要
符号回归搜索通常使用遗传编程近似数据集的函数形式。 由于通常不限制该函数的形式，因此由于非线性函数链或长表达式，遗传编程可能会返回难以理解的模型。最近提出了一种称为相互作用转变的新颖代表，以减轻此问题。在此表示形式中，函数形式仅限于将单个单变量函数应用于所选变量的相互作用的应用项的仿射组合。该表示形式获得了标准基准的竞争解决方案。尽管取得了最初的成功，但更广泛的基准测试功能揭示了约束表示的局限性。 在本文中，我们提出了对该表示形式的扩展，称为Troncoramation-interaction Rational Contration表示，将新函数形式定义为两个相互作用变换函数的合理形式。另外，目标变量也可以通过单变量函数进行转换。主要目标是提高近似能力，同时仍限制表达式的整体复杂性。 我们通过带有交叉和突变的标准遗传编程测试了这种表示。与其前身和大型基准的最先进性能相比，结果显示出了很大的进步。
Symbolic Regression searches for a function form that approximates a dataset often using Genetic Programming. Since there is usually no restriction to what form the function can have, Genetic Programming may return a hard to understand model due to non-linear function chaining or long expressions. A novel representation called Interaction-Transformation was recently proposed to alleviate this problem. In this representation, the function form is restricted to an affine combination of terms generated as the application of a single univariate function to the interaction of selected variables. This representation obtained competing solutions on standard benchmarks. Despite the initial success, a broader set of benchmarking functions revealed the limitations of the constrained representation. In this paper we propose an extension to this representation, called Transformation-Interaction-Rational representation that defines a new function form as the rational of two Interaction-Transformation functions. Additionally, the target variable can also be transformed with an univariate function. The main goal is to improve the approximation power while still constraining the overall complexity of the expression. We tested this representation with a standard Genetic Programming with crossover and mutation. The results show a great improvement when compared to its predecessor and a state-of-the-art performance for a large benchmark.
