Support vector regression with noisy data: a second order cone programming approach
A robust convex optimization approach is proposed for support vector regression (SVR) with noisy input data. The data points are assumed to be uncertain, but bounded within given hyper-spheres of radius eta. The proposed Robust SVR model is equivalent to a Second Order Cone Programming (SOCP) problem. SOCP formulation with Gaussian noise models assumption is discussed. Computational results are presented both on real world and synthetic data sets. The robust SOCP approach is compared with several other regression algorithms such as SVR, least-square SVR, and artificial neural networks by injecting Gaussian noise to each of the data points. The proposed approach out performs the other regression algorithms for some data sets. Moreover, the generalization behavior of the SOCP method is better than the traditional SVR with increasing the uncertainty level eta until a threshold value.
regression robustness optimization parameter estimation kernel functions support vector machines