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<p>Functional regression analysis is crucial in functional data analysis (FDA). Existing methods primarily focus on one-dimensional functional data and often rely on the linear relationships between predictors and the response, which may not hold in real-world applications. Additionally, the inclusion of insignificant functional predictors can reduce predictive accuracy and hinder interpretability. This paper proposes a novel neural network-based functional nonlinear regression method for multiple multidimensional predictors. The method effectively predicts the response and performs variable selection. We explore the universal approximation property of the network and prove the consistency of variable selection. Simulation studies and two real-world datasets demonstrate the superiority of our method. Furthermore, an open-source Python package, <Emphasis FontCategory="NonProportional">mfdnn</Emphasis>, has been developed to facilitate implementation.</p>

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Variable selection in multidimensional functional nonlinear regression using neural networks

  • 期刊论文

  • 发表日期：

    2026年6月1日

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  • Dongxue Wang,
  • Jingxiao Zhang,
  • Rou Zhong

摘要

Functional regression analysis is crucial in functional data analysis (FDA). Existing methods primarily focus on one-dimensional functional data and often rely on the linear relationships between predictors and the response, which may not hold in real-world applications. Additionally, the inclusion of insignificant functional predictors can reduce predictive accuracy and hinder interpretability. This paper proposes a novel neural network-based functional nonlinear regression method for multiple multidimensional predictors. The method effectively predicts the response and performs variable selection. We explore the universal approximation property of the network and prove the consistency of variable selection. Simulation studies and two real-world datasets demonstrate the superiority of our method. Furthermore, an open-source Python package, mfdnn, has been developed to facilitate implementation.