Proximal <i>LSSVR</i> of Gauss-Laplacian With Mixed-Noise-Characteristics and Its Applications for Short-Term Wind-Speed Forecasting

Proximal least squares support vector regression (PLSSVR) is a novel regression machine that combines the advantages of proximal support vector regression (PSVR) and least squares support vector regression (LSSVR). It possesses the traits of high efficiency, simplicity, and good generalization ability. This article establishes a new regression model by utilizing the above model frameworks, called PLSSVR model of heteroscedastic Gauss-Laplacian with mixed-noise-characteristics (PLSSVR-GLMH). The least square method is introduced and the regularization terms <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${(1/2)}\cdot b_{t} ^{2}$ </tex-math></inline-formula> are added in model PLSSVR-GLMH respectively. It converts inequality constraint problems into simpler equality constraint problems and employs the Augmented Lagrange multiplier method to solve the proposed model. This not only improves the training speed and generalization ability, but also effectively enhances the prediction accuracy. Because the wind-speed forecasting error approximately conforms to the Gauss-Laplacian mixture noise distribution, in the real-world wind-speed dataset, the prediction accuracy of the PLSSVR-GLM model was significantly improved compared to the PLSSVR and LSSVR-GLM models. The experimental results validate the efficacy and practicality of the proposed method.