Robust kernel-free support vector regression based on optimal margin distribution

摘要

Support vector machines have been proven to be useful for regression analysis and forecasting. When stochastic uncertainty is involved in the datasets, robust support vector regression (SVR) models are useful. In this study, we proposed a kernel-free quadratic surface support vector regression (QSSVR) model based on optimal margin distribution (OMD). This model minimizes the variance of the functional margins of all data points to achieve better generalization capability. When the data points exhibit stochastic uncertainty (without the assumption of any specific distribution), the covariance information of noise is employed to construct a robust OMD-based QSSVR (RQSSVR-OMD) model, with a set of probabilistic constraints to ensure its worst-case performance. Moreover, the probabilistic constraints in the proposed model are proven to be equivalently reformulated as second-order cone constraints for efficient implementation. Extensive computational experiments on public benchmark datasets were conducted to demonstrate the superior performance of the proposed RQSSVR-OMD model over other well-established SVR models in terms of forecasting accuracy and time. The proposed model was also validated to successfully handle real-life uncertain battery data for battery power-consumption forecasting.