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<p>Mixtures of linear experts (MoE) provide a flexible framework for modeling heterogeneous regression relationships and are widely used in classification and clustering. However, classical MoE formulations are sensitive to outliers and may yield biased inference when responses are subject to censoring. To address these limitations, we propose a robust MoE model for censored responses in which expert-level errors follow the normal mean–variance mixture (NMVM) family. This formulation accommodates censoring, skewness, and heavy-tailed behavior within a unified likelihood-based framework. Identifiability of the proposed model, up to label switching, is established under mild and interpretable regularity conditions. Parameter estimation is performed via an expectation–conditional maximization (ECME) algorithm, ensuring stable estimation and monotonic improvement of the observed-data likelihood. Extensive simulation studies and a real data application demonstrate that the proposed MoE–NMVM–CR model achieves improved robustness, accurate parameter estimation, and competitive clustering performance relative to existing censored MoE and censored mixture regression approaches, while remaining computationally tractable.</p>

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Robust expert mixtures: handling censored data with normal mean-variance mixture distributions

  • 期刊论文

  • 发表日期：

    2026年7月1日

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  • T. Manouchehri,
  • F. Setoudehtazangi,
  • A. R. Nematollahi,
  • G. McLachlan

摘要

Mixtures of linear experts (MoE) provide a flexible framework for modeling heterogeneous regression relationships and are widely used in classification and clustering. However, classical MoE formulations are sensitive to outliers and may yield biased inference when responses are subject to censoring. To address these limitations, we propose a robust MoE model for censored responses in which expert-level errors follow the normal mean–variance mixture (NMVM) family. This formulation accommodates censoring, skewness, and heavy-tailed behavior within a unified likelihood-based framework. Identifiability of the proposed model, up to label switching, is established under mild and interpretable regularity conditions. Parameter estimation is performed via an expectation–conditional maximization (ECME) algorithm, ensuring stable estimation and monotonic improvement of the observed-data likelihood. Extensive simulation studies and a real data application demonstrate that the proposed MoE–NMVM–CR model achieves improved robustness, accurate parameter estimation, and competitive clustering performance relative to existing censored MoE and censored mixture regression approaches, while remaining computationally tractable.