Multivariate polynomial regression by an explainable sigma-pi neural network

Xiaoxiang Guo; Zuolin Shi; Bin Li; Xiaoxiang Guo; Zuolin Shi; Bin Li

doi:10.3934/bdia.2024004

Big Data and Information Analytics

2024, Volume 8, 65-79. doi: 10.3934/bdia.2024004

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Research article

Multivariate polynomial regression by an explainable sigma-pi neural network

1.
School of Mathematics and Statistics, Henan Academy of Big Data, Zhengzhou University, Zhengzhou 450001, China
2.
School of Water Conservancy and Transportation, Zhengzhou University, Zhengzhou 450001, China

Received: 17 September 2024 Revised: 14 October 2024 Accepted: 17 October 2024 Published: 30 October 2024

Over the years, data-driven regression on univariate functions has been extensively studied. However, fast, effective, and stable algorithms for multivariate function fitting are still lacking. Recently, Kolmogorov-Arnold networks have garnered significant attention among scholars due to their superior accuracy and interpretability compared to multi-layer perceptrons. In this paper, we have demonstrated that the sigma-pi neural network, a form of Kolmogorov-Arnold networks, can efficiently fit multivariate polynomial functions, including fractional-order multivariate polynomials. Three examples were employed to illustrate the regression performance of the designed neural networks. The explainable sigma-pi neural network will lay the groundwork for further development of general tools for multivariate nonlinear function regression problems.
- data-driven,
- fitting,
- interpretability,
- sigma-pi neural network,
- multivariate polynomial
Citation: Xiaoxiang Guo, Zuolin Shi, Bin Li. Multivariate polynomial regression by an explainable sigma-pi neural network[J]. Big Data and Information Analytics, 2024, 8: 65-79. doi: 10.3934/bdia.2024004

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Abstract

Over the years, data-driven regression on univariate functions has been extensively studied. However, fast, effective, and stable algorithms for multivariate function fitting are still lacking. Recently, Kolmogorov-Arnold networks have garnered significant attention among scholars due to their superior accuracy and interpretability compared to multi-layer perceptrons. In this paper, we have demonstrated that the sigma-pi neural network, a form of Kolmogorov-Arnold networks, can efficiently fit multivariate polynomial functions, including fractional-order multivariate polynomials. Three examples were employed to illustrate the regression performance of the designed neural networks. The explainable sigma-pi neural network will lay the groundwork for further development of general tools for multivariate nonlinear function regression problems.

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