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<p>While the mixture of linear experts models are widely used for capturing heterogeneity in regression and clustering, their traditional Gaussian based formulations often fail with skewed, heavy tailed, or outlier contaminated data. This paper develops a robust mixture of linear experts (MoLE) framework based on normal mean–variance mixture (NMVM) distributions, explicitly modeling both asymmetric probability structures and heterogeneous tail behavior across expert components. The proposed estimation framework employs an optimized ECME algorithm that simultaneously enhances computational efficiency and estimation accuracy. Through extensive simulation studies, we demonstrate the model’s accuracy and robustness under challenging data conditions. Applications to real datasets, including musical tone perception and U.S. county level poverty analysis, highlight the model’s practical advantages in both predictive performance and interpretability. These results suggest that the NMVM–MoLE framework is a powerful and adaptable tool for analyzing real world data with nonstandard distributional features.</p>

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Robust linear experts model with normal mean–variance mixtures

  • 期刊论文

  • 发表日期：

    2026年6月22日

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  • F. Setoudehtazangi,
  • T. Manouchehri,
  • A. R. Nematollahi,
  • D. Wraith

摘要

While the mixture of linear experts models are widely used for capturing heterogeneity in regression and clustering, their traditional Gaussian based formulations often fail with skewed, heavy tailed, or outlier contaminated data. This paper develops a robust mixture of linear experts (MoLE) framework based on normal mean–variance mixture (NMVM) distributions, explicitly modeling both asymmetric probability structures and heterogeneous tail behavior across expert components. The proposed estimation framework employs an optimized ECME algorithm that simultaneously enhances computational efficiency and estimation accuracy. Through extensive simulation studies, we demonstrate the model’s accuracy and robustness under challenging data conditions. Applications to real datasets, including musical tone perception and U.S. county level poverty analysis, highlight the model’s practical advantages in both predictive performance and interpretability. These results suggest that the NMVM–MoLE framework is a powerful and adaptable tool for analyzing real world data with nonstandard distributional features.