Robust approximation of the conditional mean for applications of Machine Learning

Abstract

Machine Learning approaches are increasingly used in a range of applications. They are shown to produce low conventional errors but in many real applications fail to model the underlying input–output relationships. This is because the error measures used only predict the conditional mean under some restrictive assumptions, often not met by the data we extract from applications. However, new approaches to Machine Learning, for example using Evolutionary Computation, allow a range of alternative error measures to be used. This paper explores the use of the Fit to Median Error measure in machine learning regression automation, using evolutionary computation in order to improve the approximation of the ground truth. When used alongside conventional error measures it improves the robustness of the learnt input–output relationships to the conditional median. It is compared to traditional regularisers to illustrate that the use of the Fit to Median Error produces regression neural networks which model more consistent input–output relationships. The problem considered is ship power prediction using a fuel-saving air lubrication system, which is highly stochastic in nature. The networks optimised for their Fit to Median Error are shown to approximate the ground truth more consistently, without sacrificing conventional Minkowski-r error values.