Robust mixture regression with Exponential Power distribution

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.