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

The paper presents Taylor Map Polynomial Neural Network (TMPNN), a novel form of very high-order polynomial regression, in which the same coefficients for a lower-to-moderateorder polynomial regression are iteratively reapplied so as to achieve a higher-order model without the number of coefficients to be fit exploding in the usual curse-of-dimensionality way. This method naturally implements multi-target regression and can capture internal relationships be-tween targets. We also introduce an approach for model interpretation in the form of systems of differential equations. By benchmarking on Feynman regression, UCI, Friedman-1, and real-life industrial datasets, we demonstrate that the proposed method performs comparably to the state-of-the-art regression methods and outperforms them on specific tasks.