TMPNN: High-Order Polynomial Regression Based on Taylor Map Factorization

TL;DR

This paper introduces TMPNN, a high-order polynomial regression method based on Taylor map factorization, capable of multi-target regression and interpretable as differential equations, with competitive performance on benchmark datasets.

Contribution

The paper proposes a novel high-order polynomial regression approach using Taylor map factorization, enabling multi-target regression and interpretability through differential equations.

Findings

Performs comparably to state-of-the-art methods on benchmark datasets.

Outperforms existing methods on specific regression tasks.

Demonstrates effective modeling of nonlinear patterns with high-order polynomials.

Abstract

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.