TMPNN: High-Order Polynomial Regression Based on Taylor Map
  Factorization
Andrei Ivanov Stefan Maria Ailuro
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.