Shifted asymmetric Laplace mixtures of experts

TL;DR

This paper introduces a robust mixture of experts model using the shifted asymmetric Laplace distribution to handle skewed, heavy-tailed data, with a novel hybrid EM-MM algorithm for parameter estimation.

Contribution

It proposes the SALMoE model for robust regression and clustering, overcoming Gaussian MoE limitations, and develops a hybrid EM-MM algorithm for efficient estimation.

Findings

The SALMoE model effectively handles skewed and heavy-tailed data.

The hybrid EM-MM algorithm guarantees nondecreasing log-likelihood.

Simulation and real data applications demonstrate robustness and utility.

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.