Polynomial regression is widely used and can help to express nonlinear patterns. However, considering very high polynomial orders may lead to overfitting and poor extrapolation ability for unseen data. The paper presents a method for constructing a high-order polynomial regression based on the Taylor map factorization. This method naturally implements multi-target regression and can capture internal relationships between targets. Additionally, we introduce an approach for model interpretation in the form of systems of differential equations. By benchmarking on UCI open access datasets, Feynman symbolic regression datasets, and Friedman-1 datasets, we demonstrate that the proposed method performs comparable to the state-of-the-art regression methods and outperforms them on specific tasks.

翻译：多项式回归被广泛使用，有助于表达非线性模式。然而，考虑过高的多项式阶数可能导致过拟合，并对未见数据的外推能力较差。本文提出了一种基于泰勒映射分解构建高阶多项式回归的方法。该方法天然地实现了多目标回归，并能捕捉目标之间的内在关系。此外，我们引入了一种以微分方程组形式进行模型解释的方法。通过在UCI开放数据集、费曼符号回归数据集和Friedman-1数据集上进行基准测试，我们证明该方法与最先进的回归方法性能相当，并在特定任务上优于它们。