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Interaction–Transformation Evolutionary Algorithm for Symbolic Regression
Evolutionary Computation ( IF 6.8 ) Pub Date : 2021-09-01 , DOI: 10.1162/evco_a_00285
F O de Franca 1 , G S I Aldeia 1
Affiliation  

Interaction–Transformation (IT) is a new representation for Symbolic Regression that reduces the space of solutions to a set of expressions that follow a specific structure. The potential of this representation was illustrated in prior work with the algorithm called SymTree. This algorithm starts with a simple linear model and incrementally introduces new transformed features until a stop criterion is met. While the results obtained by this algorithm were competitive with the literature, it had the drawback of not scaling well with the problem dimension. This article introduces a mutation-only Evolutionary Algorithm, called ITEA, capable of evolving a population of IT expressions. One advantage of this algorithm is that it enables the user to specify the maximum number of terms in an expression. In order to verify the competitiveness of this approach, ITEA is compared to linear, nonlinear, and Symbolic Regression models from the literature. The results indicate that ITEA is capable of finding equal or better approximations than other Symbolic Regression models while being competitive to state-of-the-art nonlinear models. Additionally, since this representation follows a specific structure, it is possible to extract the importance of each original feature of a data set as an analytical function, enabling us to automate the explanation of any prediction. In conclusion, ITEA is competitive when comparing to regression models with the additional benefit of automating the extraction of additional information of the generated models.



中文翻译:

符号回归的交互转换进化算法

交互转换 (IT) 是符号回归的一种新表示,它将解决方案的空间减少到遵循特定结构的一组表达式。这种表示的潜力在之前使用称为 SymTree 的算法的工作中得到了说明。该算法从一个简单的线性模型开始,并逐步引入新的变换特征,直到满足停止标准。虽然该算法获得的结果与文献具有竞争力,但它的缺点是不能很好地扩展问题维度。本文介绍了一种仅突变的进化算法,称为 ITEA,能够进化 IT 表达式群体。该算法的一个优点是它使用户能够指定表达式中的最大项数。为了验证这种方法的竞争力,将ITEA与文献中的线性、非线性和符号回归模型进行了比较。结果表明,ITEA 能够找到与其他符号回归模型相同或更好的近似值,同时与最先进的非线性模型具有竞争力。此外,由于这种表示遵循特定的结构,因此可以提取数据集的每个原始特征的重要性作为分析函数,使我们能够自动解释任何预测。总之,与回归模型相比,ITEA 具有竞争力,它具有自动提取生成模型的附加信息的额外好处。结果表明,ITEA 能够找到与其他符号回归模型相同或更好的近似值,同时与最先进的非线性模型具有竞争力。此外,由于这种表示遵循特定的结构,因此可以提取数据集的每个原始特征的重要性作为分析函数,使我们能够自动解释任何预测。总之,与回归模型相比,ITEA 具有竞争力,它具有自动提取生成模型的附加信息的额外好处。结果表明,ITEA 能够找到与其他符号回归模型相同或更好的近似值,同时与最先进的非线性模型具有竞争力。此外,由于这种表示遵循特定的结构,因此可以提取数据集的每个原始特征的重要性作为分析函数,使我们能够自动解释任何预测。总之,与回归模型相比,ITEA 具有竞争力,它具有自动提取生成模型的附加信息的额外好处。可以提取数据集的每个原始特征的重要性作为分析函数,使我们能够自动解释任何预测。总之,与回归模型相比,ITEA 具有竞争力,它具有自动提取生成模型的附加信息的额外好处。可以提取数据集的每个原始特征的重要性作为分析函数,使我们能够自动解释任何预测。总之,与回归模型相比,ITEA 具有竞争力,它具有自动提取生成模型的附加信息的额外好处。

更新日期:2021-09-12
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