Robust mixture regression using mean-shift penalisation

Abstract

The purpose of finite mixture regression (FMR) is to model the relationship between a response and feature variables in the presence of latent groups in the population. The different regression structures are quantified by the unique parameters of each latent group. The Gaussian mixture regression model is a method commonly used in FMR since it simplifies the estimation and interpretation of the model output. However, it is highly affected if outliers are present in the data. Failing to account for the outliers may distort the results and lead to inappropriate conclusions. We consider a mean-shift robust mixture regression approach to address this. This method uses a component specific mean-shift parameterisation which contributes towards both the successful identification of outliers as well as robust parameter estimation. The technique is demonstrated by a simulation study and a real-world application. The mean-shift regression method proves to be highly robust against outliers.