Prediction intervals in supervised learning for model evaluation and discrimination

Abstract

In this paper we explore prediction intervals and how they can be used for model evaluation and discrimination in the supervised regression setting of medium sized datasets. We review three different methods for making prediction intervals and the statistics used for their evaluation. How the prediction intervals look like, how different methods behave and how the prediction intervals can be utilized for the graphical evaluation of models is illustrated with the help of simple datasets. Afterwards we propose a combined method for making prediction intervals and explore its performance with two voting schemes for combining predictions of a diverse ensemble of models. All methods are tested on a large set of datasets on which we evaluate individual methods and aggregated variants for their abilities of selecting the best predictions. The analysis of correlations between the root mean squared error and our evaluation statistic show that both stability and reliability of the results increase as the techniques get more elaborate. We confirm that the methodology is suitable for the graphical comparison of individual models and is a viable way of discriminating among model candidates.