A critical review of multi-output support vector regression

Abstract

Single-output regression is a widely used statistical modeling method to predict an output based on one or more features of a datapoint. If a dataset has multiple outputs, they can be predicted independently from each other although this disregards potential correlations and thus may negatively affect the predictive performance. Therefore, multi-output regression methods predict multiple outputs simultaneously. One way to approach single-output regression is by using methods based on support vectors such as support vector regression (SVR) or least-squares SVR (LS-SVR). Based on these two, previous works have devised multi-output support vector regression methods. In this review, we introduce a unified notation to summarize the single-output support vector regression methods SVR and LS-SVR as well as state-of-the-art multi-output support vector regression methods. Furthermore, we implemented a workflow for subject- and record-wise bootstrapping and nested cross-validation experiments, which we used for an exhaustive evaluation of all single- and multi-output support vector regression methods on synthetic and non-synthetic datasets. Although the reviewed papers claim that their multi-output methods improve regression performance, we find that none of them outperform both single-output methods SVR and LS-SVR for various reasons. Due to these results, we reflected about the general concept of support vector regression and then concluded that support vector regression methods do not appear to be suitable for the task of multi-output regression.