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<p>Bayesian quantile regression, as one of the crucial tools in statistical learning, usually considers covariates in the form of vectors and matrices. However, with the development of technology and changing needs, tensor data has gradually become visible in people’s view and is now widely used in various fields. Therefore, we generalize the quantile regression model to Bayesian tensor quantile regression model and propose a Gibbs sampling method based on Tucker decomposition. Since the regularization method can effectively improve the accuracy of parameter estimation, we propose a Bayesian tensor quantile regression model with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ell_1\)</EquationSource> </InlineEquation> penalty for solving the tensor parameter and optimizing the related algorithm. Finally, we show the excellent performance of the proposed algorithms through some numerical simulations, and prove the effectiveness and feasibility of our proposed methods in real examples by applying them on the complaint Telephone Data of a prefecture-level city in China and Air quality data for Beijing in 2016.</p>

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Bayesian inference approaches for tensor quantile regression and its application

  • 期刊论文

  • 发表日期：

    2025年11月20日

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  • Zhichuan Zhu,
  • Jingxiang Huang,
  • Niansheng Tang

摘要

Bayesian quantile regression, as one of the crucial tools in statistical learning, usually considers covariates in the form of vectors and matrices. However, with the development of technology and changing needs, tensor data has gradually become visible in people’s view and is now widely used in various fields. Therefore, we generalize the quantile regression model to Bayesian tensor quantile regression model and propose a Gibbs sampling method based on Tucker decomposition. Since the regularization method can effectively improve the accuracy of parameter estimation, we propose a Bayesian tensor quantile regression model with \(\ell_1\) penalty for solving the tensor parameter and optimizing the related algorithm. Finally, we show the excellent performance of the proposed algorithms through some numerical simulations, and prove the effectiveness and feasibility of our proposed methods in real examples by applying them on the complaint Telephone Data of a prefecture-level city in China and Air quality data for Beijing in 2016.