Sphiwe B. Skhosana | Searcharxiv

arXiv2026

Shifted asymmetric Laplace mixtures of experts

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.

stat.ME↗

arXiv2026

Robust semi-parametric mixtures of linear experts using the contaminated Gaussian distribution

Semi- and non-parametric mixture of regressions are a very useful flexible class of mixture of regressions in which some or all of the parameters are non-parametric functions of the covariates. These models are, however, based on the Gaussian assumption of the component error distributions. Thus, their estimation is sensitive to outliers and heavy-tailed error distributions. In this paper, we propose semi- and non-parametric contaminated Gaussian mixture of regressions to robustly estimate the parametric and/or non-parametric terms of the models in the presence of mild outliers. The virtue of using a contaminated Gaussian error distribution is that we can simultaneously perform model-based clustering of observations and model-based outlier detection. We propose two algorithms, an expectation-maximization (EM)-type algorithm and an expectation-conditional-maximization (ECM)-type algorithm, to perform maximum likelihood and local-likelihood kernel estimation of the parametric and non-parametric of the proposed models, respectively. The robustness of the proposed models is examined using an extensive simulation study. The practical utility of the proposed models is demonstrated using real data.

stat.ME↗

arXiv2026

Nonparametric contaminated Gaussian mixture of regressions

Semi- and non-parametric mixture of regressions are a very useful flexible class of mixture of regressions in which some or all of the parameters are non-parametric functions of the covariates. These models are, however, based on the Gaussian assumption of the component error distributions. Thus, their estimation is sensitive to outliers and heavy-tailed error distributions. In this paper, we propose semi- and non-parametric contaminated Gaussian mixture of regressions to robustly estimate the parametric and/or non-parametric terms of the models in the presence of mild outliers. The virtue of using a contaminated Gaussian error distribution is that we can simultaneously perform model-based clustering of observations and model-based outlier detection. We propose two algorithms, an expectation-maximization (EM)-type algorithm and an expectation-conditional-maximization (ECM)-type algorithm, to perform maximum likelihood and local-likelihood kernel estimation of the parametric and non-parametric of the proposed models, respectively. The robustness of the proposed models is examined using an extensive simulation study. The practical utility of the proposed models is demonstrated using real data.

stat.ME↗

arXiv2026

Model-based clustering using a new mixture of circular regressions

Regression models, where the response variable is circular, are common in areas such as biology, geology and meteorology. A typical model assumes that the conditional distribution of the response follows a von-Mises distribution. However, this assumption is inadequate when the response variable is multimodal. For this reason, in this paper, a finite mixture of regressions model is proposed for the case of a circular response variable and a set of circular and/or linear covariates. Mixture models are very useful when the underlying population is multimodal. Despite the prevalence of multimodality in regression modelling of circular data, the use of mixtures of regressions has received no attention in the literature. This paper aims to close this knowledge gap. To estimate the proposed model, we develop a maximum likelihood estimation procedure via the Expectation-Maximization algorithm. An extensive simulation study is used to demonstrate the practical use and performance of the proposed model and estimation procedure. In addition, the model is shown to be useful as a model-based clustering tool. Lastly, the model is applied to a real dataset from a wind farm in South Africa.

stat.ME↗