基于非参数极大似然的半参数鲁棒专家混合模型
Semiparametric robust mixture of experts based on nonparametric maximum likelihood
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中文总结 AI 辅助
该研究针对现有MoE模型对误差分布参数假设敏感的问题，提出基于非参数极大似然的半参数鲁棒MoE模型，可提升复杂误差下的鲁棒性且在高斯设定下仍具竞争力。
中文摘要 AI 辅助
专家混合（MoE）模型通过门控网络实现协变量依赖的混合，为建模异质回归关系提供了灵活方法，但多数现有MoE模型对专家误差分布依赖参数假设（通常为高斯分布），当假设误设时会导致效率低下，且对异常值或重尾行为敏感。本文提出一种半参数MoE模型，其中每个专家的误差分布表示为通过非参数极大似然估计的非参数高斯尺度混合，在保留MoE框架的可解释性与结构的同时，放宽了高斯尺度混合类内的参数假设。该模型可适配复杂误差结构，在受污染和重尾情况下提升鲁棒性，且在高斯假设设定正确时仍具竞争力，为参数MoE公式提供了兼具实用性与理论基础的替代方案。
英文摘要
The mixture of experts (MoE) model provides a flexible approach for modeling heterogeneous regression relationships by allowing covariate-dependent mixing through a gating network, but most existing MoE models rely on parametric assumptions for expert error distributions, typically Gaussian, which can lead to inefficiency and sensitivity to outliers or heavy-tailed behavior when misspecified. We propose a semiparametric MoE model in which each expert error distribution is represented as a nonparametric Gaussian scale mixture estimated via nonparametric maximum likelihood, relaxing parametric assumptions within the Gaussian scale-mixture class while preserving the interpretability and structure of the MoE framework. The resulting model adapts to complex error structures, improves robustness under contamination and heavy tails, and remains competitive under well-specified Gaussian settings, providing a practical and theoretically grounded alternative to parametric MoE formulations.
