Robust mixture regression with Exponential Power distribution

TL;DR

This paper develops a robust mixture regression model assuming an exponential power distribution for errors, enhancing outlier resistance and interpretability compared to Gaussian mixtures.

Contribution

It extends mixture regression analysis to exponential power distributions, providing a robust and easily implementable model selection method.

Findings

The exponential power mixture model is more robust to outliers.

Model selection is simplified for the exponential power mixture model.

Exponential power mixtures tend to have fewer components than Gaussian mixtures.

Abstract

Assuming an exponential power distribution is one way to deal with outliers in regression and clustering, which can increase the robustness of the analysis. Gaussian distribution is a special case of an exponential distribution. And an exponential power distribution can be viewed as a scale mixture of normal distributions. Thus, model selection methods developed for the Gaussian mixture model can be easily extended for the exponential power mixture model. Moreover, Gaussian mixture models tend to select more components than exponential power mixture models in real-world cases, which means exponential power mixture models are easier to interpret. In this paper, We develop analyses for mixture regression models when the errors are assumed to follow an exponential power distribution. It will be robust to outliers, and model selection for it is easy to implement.