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<p>The Factor Augmented Regression Model (FARM) is recently developed as a powerful tool to deal with high-dimensional correlated data. However, there is still lack of suitable methods for the FARM in a distributed system, which is becoming very common nowadays. In this article, we investigate the distributed learning of the FARM for high-dimensional data. A direct divide-and-conquer estimator by averaging all local penalized estimators is biased. We then in this paper develop two debiasing procedures for the FARM. The first approach still follows the divide-and-conquer strategy by averaging all local debiased estimators. The second approach takes a one-step estimation strategy, which reduces computational cost largely. Finally, a hard thresholding method is considered to ensure the sparsity of the proposed debiased lasso estimators. We establish the convergence rates and asymptotic normality of the proposed estimators. Through simulations and real-data experiments, we validate the finite-sample behavior of our estimators and provide practical guidelines for method selection in heterogeneous environments.</p>

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Distributed learning for high-dimensional factor augmented regression models

  • 期刊论文

  • 发表日期：

    2025年11月5日

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  • Zhen Qi,
  • Xu Guo,
  • Haobo Qi

摘要

The Factor Augmented Regression Model (FARM) is recently developed as a powerful tool to deal with high-dimensional correlated data. However, there is still lack of suitable methods for the FARM in a distributed system, which is becoming very common nowadays. In this article, we investigate the distributed learning of the FARM for high-dimensional data. A direct divide-and-conquer estimator by averaging all local penalized estimators is biased. We then in this paper develop two debiasing procedures for the FARM. The first approach still follows the divide-and-conquer strategy by averaging all local debiased estimators. The second approach takes a one-step estimation strategy, which reduces computational cost largely. Finally, a hard thresholding method is considered to ensure the sparsity of the proposed debiased lasso estimators. We establish the convergence rates and asymptotic normality of the proposed estimators. Through simulations and real-data experiments, we validate the finite-sample behavior of our estimators and provide practical guidelines for method selection in heterogeneous environments.