Twin Least Squares Support Vector Regression of Heteroscedastic Gaussian Noise Model

The training algorithm of twin least squares support vector regression (TLSSVR) transforms unequal constraints into equal constraints in a pair of quadratic programming problems, it owns faster computational speed. The classical least squares support vector regression (LSSVR) assumpt that the noise is Gaussian with zero mean and the homoscedastic variance. However, it is found that the noise models in some practical applications satisfy Gaussian distribution with zero mean and heteroscedastic variance. In this paper, the LSSVR is combined with the twin hyperplanes, and then an optimal loss function for Gaussian noise with heteroscedasticity is introduced, which is called the twin least squares support vector regression with heteroscedastic Gaussian noise (TLSSVR-HGN). Like LSSVR, TLSSVR-HGN also lacks sparsity. To analyze the generalization ability of the proposed model, the sparse TLSSVR-HGN (STLSSVR-HGN) is proposed with a simple mechanism. The proposed model has been verified using the artificial data set, several benchmark data sets and actual wind speed data. The experimental results show that TLSSVR-HGN is a better technology than the other algorithms.