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<p>Deep learning approaches have achieved great success in both applications and theoretical studies in recent years. In this paper, we study a partially linear regression model for longitudinal data, with the nonparametric component approximated by a deep neural network. The proposed method circumvents the curse of dimensionality while facilitating the interpretability of linear effects. A maximum likelihood estimation approach is introduced, and a two-step iterative algorithm is developed for optimization. The convergence rate and the asymptotic properties of the resulting estimator are established. The performance of the method is demonstrated through simulation studies and an application to a yeast cell-cycle gene expression dataset.</p>

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A partially linear model for longitudinal data using deep neural networks

  • 期刊论文

  • 发表日期：

    2026年6月23日

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  • Bokai Zhang,
  • Mengqi Xie,
  • Jie Zhou,
  • Ziyuan Wei

摘要

Deep learning approaches have achieved great success in both applications and theoretical studies in recent years. In this paper, we study a partially linear regression model for longitudinal data, with the nonparametric component approximated by a deep neural network. The proposed method circumvents the curse of dimensionality while facilitating the interpretability of linear effects. A maximum likelihood estimation approach is introduced, and a two-step iterative algorithm is developed for optimization. The convergence rate and the asymptotic properties of the resulting estimator are established. The performance of the method is demonstrated through simulation studies and an application to a yeast cell-cycle gene expression dataset.