Support Vector Regression with Imprecise Observations

Support vector classification (SVC) and support vectors regression (SVR) are learning machines that have excellent generalization performance. The data which used by classical statistical learning theory is assumed precise. However, the data from real world sometimes low-quality or imprecise, the uncertainty theory and uncertain statistics are appropriate methods to process the imprecise observations. In this paper, the optimal hyperplane under the framework of uncertainty theory be put forward as the basis of SVR. Based on the definition of optimal hyperplane, the theorem of SVR with imprecise observation be proposed, this theorem obtains the basic ideology and dual problem, can solves the support vector problem under the uncertainty theory. Moreover, the cross-validation (CV) method and the average test error (ATE) be employed to evaluate the generalization performance of regression models. After evaluation of models, the forecast value can be computed and the root mean squared error (RMSE) be used to measure the effect of prediction. Finally, a numerical example be given to show the excellent performance of SVR, SVR has the minimum ATE and RMSE among some models, then the forecast value of the test set be calculated.