Regression as classification

The paper presents how solving regression problems can be posed as finding solutions to multiclass classification tasks. The accuracy (averaged over several benchmarking data sets used in this study) of an approximating (hyper)surface to the data points over a given high-dimensional input space created by a nonlinear multiclass classifier is slightly superior to the solution obtained by regression (hyper)surface. In terms of the CPU time needed for training i.e., for tuning the hyperparameters of the models, the nonlinear classifier shows significant (order of magnitudes for large datasets) advantages too. Here, the support vector machine (SVM) has been solving given regression problems as a classic SVM regressor and as the SVM classifier. In order to transform a regression problem into a classification task two possible discretizations of a continuous output (target) vector y are presented and compared. A very strict double (nested) cross-validation technique has been used for measuring performances of regression and multiclass classification SVMs. A novel approach and the experimental results obtained for five benchmarking regression data sets warrant both further theoretical investigations and broad application in practice.