Shifted asymmetric Laplace mixtures of experts

2026-05-03

AI Summary

This study addresses the limitations of conventional Gaussian mixture-of-experts models when applied to skewed, heavy-tailed, or outlier-contaminated data. To enhance robustness and modeling flexibility, the authors propose a novel mixture-of-experts framework based on the translated asymmetric Laplace distribution—a distribution introduced here for the first time into the mixture-of-experts paradigm. Parameter estimation is carried out via a hybrid EM-MM algorithm that integrates the Minorization–Maximization (MM) and Expectation–Maximization (EM) approaches, guaranteeing monotonic non-decrease of the observed log-likelihood. Extensive simulations and experiments on real-world economic datasets demonstrate that the proposed method achieves superior robustness and practical utility in both regression and clustering tasks under non-Gaussian conditions.

Abstract

Mixtures of experts (MoE) models provide a flexible framework for modelling heterogeneity in data for regression and model-based clustering and classification. MoE models for regression are typically based on the Gaussian assumption for the expert distributions. To robustify the MoE framework with respect to data exhibiting skewness, heavy tails and outliers, we propose a robust non-normal MoE model using the shifted asymmetric Laplace (SAL) distribution. The proposed SALMoE model overcomes the limitations of the Gaussian MoE model when the observed data are asymmetric and heavy-tailed. Through a combination of the minorization-maximization (MM) algorithm with the classical Expectation-Maximization (EM), we develop a dedicated hybrid EM-MM algorithm to estimate the parameters of the SALMoE model. The EM-MM algorithm is shown to yield a nondecreasing observed log-likelihood. A simulation study demonstrates the robustness and practical utility of the proposed model. Finally, the SALMoE model is applied to two real-world economic datasets.

Problem

• Mixtures of Experts
• Shifted Asymmetric Laplace
• Robust Regression
• Heavy-tailed Data
• Skewed Data

Innovation

• Shifted Asymmetric Laplace
• Mixtures of Experts
• Robust Regression
• EM-MM Algorithm
• Heavy-tailed Data