General noise support vector regression with non-constant uncertainty intervals for solar radiation prediction

General noise cost functions have been recently proposed for support vector regression (SVR). When applied to tasks whose underlying noise distribution is similar to the one assumed for the cost function, these models should perform better than classical є-SVR. On the other hand, uncertainty estimates for SVR have received a somewhat limited attention in the literature until now and still have unaddressed problems. Keeping this in mind, three main goals are addressed here. First, we propose a framework that uses a combination of general noise SVR models with naive online R minimization algorithm (NORMA) as optimization method, and then gives nonconstant error intervals dependent upon input data aided by the use of clustering techniques. We give theoretical details required to implement this framework for Laplace, Gaussian, Beta, Weibull and Marshall–Olkin generalized exponential distributions. Second, we test the proposed framework in two real-world regression problems using data of two public competitions about solar energy. Results show the validity of our models and an improvement over classical є-SVR. Finally, in accordance with the principle of reproducible research, we make sure that data and model implementations used for the experiments are easily and publicly accessible.
With partial support from Spain’s grants TIN2013-42351-P, TIN2016-76406-P, TIN2015-70308-REDT, as well as S2013/ICE-2845 CASI-CAM-CM. This work was supported also by project FACIL–Ayudas Fundación BBVA a Equipos de Investigación Científica 2016 and the UAM–ADIC Chair for Data Science and Machine Learning. We gratefully acknowledge the use of the facilities of Centro de Computación Científica, CCC, at Universidad Autónoma de Madrid, UAM