Machine Learning Alternatives to Response Surface Models

Abstract

In the Design of Experiments, we seek to relate response variables to explanatory factors. Response Surface methodology (RSM) approximates the relation between output variables and a polynomial transform of the explanatory variables using a linear model. Some researchers have tried to adjust other types of models, mainly nonlinear and nonparametric. We present a large panel of Machine Learning approaches that may be good alternatives to the classical RSM approximation. The state of the art of such approaches is given, including classification and regression trees, ensemble methods, support vector machines, neural networks and also direct multi-output approaches. We survey the subject and illustrate the use of ten such approaches using simulations and a real use case. In our simulations, the underlying model is linear in the explanatory factors for one response and nonlinear for the others. We focus on the advantages and disadvantages of the different approaches and show how their hyperparameters may be tuned. Our simulations show that even when the underlying relation between the response and the explanatory variables is linear, the RSM approach is outperformed by the direct neural network multivariate model, for any sample size (<50) and much more for very small samples (15 or 20). When the underlying relation is nonlinear, the RSM approach is outperformed by most of the machine learning approaches for small samples (n ≤ 30).