Single and Multi-objective Genetic Programming Methods for Prediction Intervals

Abstract

A PI is the range of values in which the real target value of a supervised learning task is expected to fall into, and it should combine two contrasting properties: to be as narrow as possible, and to include as many data observations as possible. This article presents an study on modelling Prediction Intervals (PI) with two Genetic Programming (GP) methods. The first proposed GP method is called CWC-GP, and it evolves simultaneously the lower and upper boundaries of the PI using a single fitness measure. This measure is the Coverage Width-based Criterion (CWC), which combines the width and the probability coverage of the PI. The second proposed GP method is called LUBE-GP, and it evolves independently the lower and upper boundaries of the PI. This method applies a multi-objective approach, in which one fitness aims to minimise the width and the other aims to maximise the probability coverage of the PI. Both methods were applied with the Direct and the Sequential approaches. In the former, the PI is assessed without the crisp prediction of the model. In the latter, the method makes use of the crisp prediction to find the PI boundaries. The proposed methods showed to have good potential on assessing PIs and the results pave the way to further investigations.