A preliminary study of prediction interval methods with genetic programming

This article presents an exploratory study on modelling Prediction Intervals (PI) with two Genetic Programming (GP) methods. A PI is the range of values in which the real target value is expected to fall into. It should combine two contrasting properties: to be as narrow as possible and to include as many data observations as possible. One proposed GP method, called CWC-GP, evolves simultaneously the lower and upper boundaries of the PI using a single fitness measure that combines the width and the probability coverage of the PI. The other proposed GP method, called LUBE-GP, evolves independently the boundaries of the PI with 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 Direct and 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 presented preliminary results pave the way to further investigations. The most promising results were observed with the Sequential CWC-GP.